That's what it means to live in a stochastic age.
|
|
He called it SNARC: the Stochastic Neural Analog Reinforcement Calculator.
|
|
But now there is a stochastic, episodic nature to many careers.
|
|
"The news feels progressively worse and more stochastic than it used to be."
|
|
They are examples of stochastic terrorism — individually random, but these days, statistically predictable.
|
|
To do this, I borrowed a methodology from productivity and efficiency analysis called stochastic frontier analysis.
|
|
These figures, using stochastic frontier methodology, avoid the distortions arising from simpler statistical methods like averages.
|
|
It said that after the massacre, terms like "stochastic terrorism" and "white supremacy" surged in searches.
|
|
"I've been working a new method of composing inspired by stochastic music and black midi," he said.
|
|
Collins' optimism continues when it comes to the stochastic oscillator at the bottom of the weekly chart.
|
|
That led Impossible to implement a new planning system, stochastic modeling, that factors in large fluctuations in demand.
|
|
Further, Cannaccord's "14-week stochastic indicator" has returned to an extreme overbought level of 98 out of 100.
|
|
Without getting too lost in the details, stochastic gradient descent is used to train the ResNet-50 model.
|
|
Moreno pointed to the chart's stochastic oscillator, a tool that measures whether a stock is overbought or oversold.
|
|
A mathematician will tell you that it's a stochastic process—a path defined by a series of random steps.
|
|
Some people have it and others don't; that's just the way it is, a spin of the stochastic wheel.
|
|
The stochastic oscillator momentum indicator in this stock is warning that the downward trend is not over, Cramer said.
|
|
The full stochastic oscillator, which measures when stocks are overbought or oversold, shows that Qualcomm is still far from being overbought.
|
|
"Stochastic" means "randomly determined," and your initial inclination may be to recoil — of course producers and investors and publishers aren't acting randomly!
|
|
Yes, yes, yes, not every time, and every stage in the pipeline is multiplied by a stochastic chance of failure, for sure.
|
|
One of the key variables in stochastic gradient descent is the learning rate — the degree by which weights change during the training process.
|
|
The 14-week stochastic indicator would have to drop to 30, a far cry from its current level of 87, says the strategist.
|
|
One such move was illustrated by a technical indicator called the full stochastic oscillator, which shows when a stock is overbought or oversold.
|
|
Finally, Garner noted that the stochastic oscillator, which measures when assets are overbought or oversold, is signaling oversold readings in gold's weekly chart.
|
|
So he worked out an algorithm, which he called the Stochastic Terminator, to help staff members select e-mails for each day's release.
|
|
We should be doing a stochastic process random probability sample of the country to find out where the hell the virus really is.
|
|
The technician based this on the action in the stochastic oscillator, a tool that shows when a stock has gotten overbought or oversold.
|
|
The technician also pointed to Disney's full stochastic oscillator, which detects whether a stock is overbought or oversold, at the bottom of the chart.
|
|
" However, the weekly stochastic indicator — a technical gauge of momentum in the market — is still "a good distance away from suggesting an intermediate-term low.
|
|
Central banks and other big economic institutions use far more complicated formulas, often grouped under the bewildering label of "dynamic stochastic general equilibrium" (DSGE) models.
|
|
Using TensorFlow and Theano, you'll learn how to build a neural network while exploring techniques such as dropout regularization and batch and stochastic gradient descent.
|
|
Anadol then used an AI algorithm known as tSNE (t-distributed stochastic neighbor embedding) to organize the data from the 1.7 million documents into visuals.
|
|
More important, despite the tendency to dot his book with such daunting phrases as "combinatorial game theory" and "stochastic equations," he tells a surprisingly captivating story.
|
|
The hypothesis is that this stochastic strife has something to do with technology and hyperconnectivity, that across the world we're experiencing the political equivalent of global warming.
|
|
"But we don't want you to think about the complex multi-GPU real-time rendering system and the custom game engine with stochastic anti-aliasing," Trowbridge says.
|
|
If you're in a party smaller than four, you'll be placed at the next open table, leading to stochastic seating arrangements that create unexpected social and cultural adjacencies.
|
|
It's called "stochastic terrorism," he writes, "in which mass communications, including social media, inspire random acts of violence that according to one description "are statistically predictable but individually unpredictable.
|
|
Gross mostly agreed with me, adding that a big challenge is helping customers who purchase services from machine intelligence startups understand what it means to rely on a stochastic product.
|
|
Its weekly chart shows fairly neutral readings for two key indicators: a momentum tracker called the Relative Strength Index and the slow stochastic oscillator, which measures buying and selling pressure.
|
|
Research into human behavior, building up expertise in the stochastic interactions of the modern urban curbside, and developing relationships and protocols with local authorities are all deeply time-consuming efforts.
|
|
We talked about this "stochastic terrorism" last October: I encountered the idea in a Friday thread from data scientist Emily Gorcenski, who used it to tie together four recent attacks.
|
|
Essentially this is a group of Near Earth Objects (NEOs) travelling the inner solar system in orbits stochastic enough to sporadically collide with nearby planets—Mars, Earth, Venus and Mercury.
|
|
This will help in detecting the stochastic gravitational wave background and in establishing an independent timing standard based on the long-term stability of the rotations of a group of millisecond pulsars.
|
|
A few weeks ago, the stochastic oscillator made a bullish crossover — when the black line goes above the red — signaling that shares of Disney could be due for a bounce, Cramer said.
|
|
This was not planned, but was rather the result of myriad colliding stochastic evolutions: state formation and the state's monopoly over violence, urbanization, the growing differentiation of occupations in increasingly complex economies.
|
|
As a result, they are more likely to attribute their own failures to themselves, rather than the fact that the world is stochastic, applications are crapshoots, and selection committees and referees have bad days.
|
|
Third, Dwyer is looking at a rather obscure technical marker called the stochastic indicator, which measures an asset's momentum by comparing its closing price to the range of its prices over a given period of time.
|
|
Target's full stochastic oscillator, which technicians use to tell whether a stock is overbought or oversold, is in "extremely overbought territory," meaning it could be due for a pullback after a rapid run higher, Cramer said.
|
|
It's actually a difficult stochastic problem, and understanding return distributions, the nature of the deal flow, the overall size of the fund and the investment horizon are some of the parameters that would go into solving it.
|
|
Through a series of deeply confusing-sounding facial matching tests (" t-distributed stochastic neighbor embedding," which "down-projects multidimensional information into two dimensions for visualization"), Dominy and his team came up with an answer: The patas monkey.
|
|
To make the situation cloudier, the stochastic relative strength index momentum indicator in Intel is flashing a bearish sign that hearkens back to Intel's more than 15-point decline from its April highs last year, Cramer said.
|
|
Exploring the ways in which technology and social tools and platforms shape contemporary human behaviors, McCarthy developed the project during an artistic residence at Stochastic Labs in San Francisco during a monthlong stay in the cradle of social media.
|
|
This happens because, in each iteration of stochastic gradient descent, more or less accidental correlations in the training data tell the network to do different things, dialing the strengths of its neural connections up and down in a random walk.
|
|
In August, Olivier Blanchard, a heavyweight macroeconomist, wrote a plea to colleagues to be less "imperialistic" about their use of dynamic stochastic general equilibrium models, adding that, for forecasting, their theoretical purity might be "more of a hindrance than a strength".
|
|
Not only did the stochastic oscillator show Micron coming out of being grossly oversold — a classic buy signal — but the Williams percent R oscillator, another tool measuring overbought and oversold conditions, indicated a possible move higher out of oversold territory.
|
|
Weather forecasts that take into account random (or "stochastic") processes make more accurate predictions for the frequency of tropical cyclones, the duration of droughts and other weather phenomena, such as the long-lasting heat spell over Europe in the summer of 2018.
|
|
The basic algorithm used in the majority of deep-learning procedures to tweak neural connections in response to data is called "stochastic gradient descent": Each time the training data are fed into the network, a cascade of firing activity sweeps upward through the layers of artificial neurons.
|
|
The term "stochastic terrorism" has been used to describe the recent rise of white supremacist violence, meaning mass and social media are used to amplify a sense of urgency in order to exhort sympathetic followers to commit acts of violence while keeping enough distance to maintain deniability.
|
|
As a deep neural network tweaks its connections by stochastic gradient descent, at first the number of bits it stores about the input data stays roughly constant or increases slightly, as connections adjust to encode patterns in the input and the network gets good at fitting labels to it.
|
|
Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization, is a science text, with a foreword by Sergey M. Bezrukov and Bart Kosko, which notably explores the relationships between stochastic resonance, suprathreshold stochastic resonance, stochastic quantization, and computational neuroscience. The book critically evaluates the field of stochastic resonance, considers various constraints and trade-offs in the performance of stochastic quantizers, culminating in a chapter on the application of suprathreshold stochastic resonance to the design of cochlear implants. The book also discusses, in detail, the relationship between dithering and stochastic resonance.
|
|
Every regular language is stochastic, and more strongly, every regular language is η-stochastic. A weak converse is that every 0-stochastic language is regular; however, the general converse does not hold: there are stochastic languages that are not regular. Every η-stochastic language is stochastic, for some 0<\eta<1. Every stochastic language is representable by a Rabin automaton.
|
|
Thus, each row of a right stochastic matrix (or column of a left stochastic matrix) is a stochastic vector. A common convention in English language mathematics literature is to use row vectors of probabilities and right stochastic matrices rather than column vectors of probabilities and left stochastic matrices; this article follows that convention.
|
|
Quantum stochastic calculus is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are of great use for modeling the random evolution of systems undergoing measurement, as in quantum trajectories. Just as the Lindblad master equation provides a quantum generalization to the Fokker–Planck equation, quantum stochastic calculus allows for the derivation of quantum stochastic differential equations (QSDE) that are analogous to classical Langevin equations. For the remainder of this article stochastic calculus will be referred to as classical stochastic calculus, in order to clearly distinguish it from quantum stochastic calculus.
|
|
A stochastic pump is a classical stochastic system that responds with nonzero, on average, currents to periodic changes of parameters. The stochastic pump effect can be interpreted in terms of a geometric phase in evolution of the moment generating function of stochastic currents.
|
|
Sylvie Méléard is a French mathematician specializing in probability theory, stochastic processes, particle systems, and stochastic differential equations. She is editor-in-chief of Stochastic Processes and Their Applications.
|
|
Stein W. Wallace and William T. Ziemba (eds.). Applications of Stochastic Programming. MPS-SIAM Book Series on Optimization 5, 2005. Applications of stochastic programming are described at the following website, Stochastic Programming Community.
|
|
For general stochastic processes strict-sense stationarity implies wide-sense stationarity but not every wide-sense stationary stochastic process is strict-sense stationary. However, for a Gaussian stochastic process the two concepts are equivalent. A Gaussian stochastic process is strict-sense stationary if, and only if, it is wide- sense stationary.
|
|
M. Haenggi. Stochastic geometry for wireless networks. Cambridge University Press, 2012. In the early 1960s a stochastic geometry modelE.
|
|
The stochastic evolution of system operators can also be defined in terms of the stochastic integration of given equations.
|
|
Stochastic forensics is a method to forensically reconstruct digital activity lacking artifacts, by analyzing emergent properties resulting from the stochastic nature of modern computers.Grier, Jonathan (2011). "Detecting data theft using stochastic forensics". Journal of Digital Investigation.
|
|
The two types of stochastic processes are respectively referred to as discrete-time and continuous-time stochastic processes. Discrete-time stochastic processes are considered easier to study because continuous-time processes require more advanced mathematical techniques and knowledge, particularly due to the index set being uncountable. If the index set is the integers, or some subset of them, then the stochastic process can also be called a random sequence. If the state space is the integers or natural numbers, then the stochastic process is called a discrete or integer-valued stochastic process.
|
|
As for regular Brownian motion, one can define stochastic integrals with respect to fractional Brownian motion, usually called "fractional stochastic integrals". In general though, unlike integrals with respect to regular Brownian motion, fractional stochastic integrals are not semimartingales.
|
|
The joining of Frederick's stochastic and crypto-stochastic approaches resulted in a paper called 'Towards a Conceptual Model for Quantum Mechanics'.
|
|
If A is row-stochastic and irreducible then the Perron projection is also row-stochastic and all its rows are equal.
|
|
Related to it is the Allen–Cahn equation, as well as the Stochastic Cahn–Hilliard Equation and the Stochastic Allen–Cahn equation.
|
|
Stochastic Models is a peer-reviewed scientific journal that publishes papers on stochastic models. It is published by Taylor & Francis. It was established in 1985 under the title Communications in Statistics. Stochastic Models and obtained its current name in 2001.
|
|
SMI is a stochastic programming modeler and solver written in C++. It can read Stochastic MPS and offers direct interfaces for constructing stochastic programs. It generates the deterministic equivalent linear program, solves it, and provides interfaces to access the scenario solutions.
|
|
It has important applications in mathematical finance and stochastic differential equations. The central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes: :Y_t=\int_0^t H_s\,dX_s, where H is a locally square-integrable process adapted to the filtration generated by X , which is a Brownian motion or, more generally, a semimartingale. The result of the integration is then another stochastic process.
|
|
A crucial distinction is between deterministic and stochastic models.A.G. Malliaris (2008). "stochastic optimal control," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract .
|
|
He is known as the co-author of an influential research monograph with Marc Yor on stochastic processes and stochastic analysis (local martingale).
|
|
In the context of mathematical construction of stochastic processes, the term regularity is used when discussing and assuming certain conditions for a stochastic process to resolve possible construction issues. For example, to study stochastic processes with uncountable index sets, it is assumed that the stochastic process adheres to some type of regularity condition such as the sample functions being continuous.
|
|
In 2003, researchers realized that these two operations could be modeled very simply with stochastic computing. Moreover, since the belief propagation algorithm is iterative, stochastic computing provides partial solutions that may lead to faster convergence. Hardware implementations of stochastic decoders have been built on FPGAs. The proponents of these methods argue that the performance of stochastic decoding is competitive with digital alternatives.
|
|
A crucial distinction is between deterministic and stochastic control models.Malliaris, A.G. (2008). "stochastic optimal control", The New Palgrave Dictionary of Economics, 2nd Edition. Abstract .
|
|
Our general setting features stochastic approximations of the cocoercive operator and stochastic perturbations in the evaluation of the resolvents of the set-valued operator.
|
|
There are a number of groups of matrices that form specializations of non-negative matrices, e.g. stochastic matrix; doubly stochastic matrix; symmetric non-negative matrix.
|
|
Any stochastic process with a countable index set already meets the separability conditions, so discrete-time stochastic processes are always separable. A theorem by Doob, sometimes known as Doob's separability theorem, says that any real-valued continuous-time stochastic process has a separable modification. Versions of this theorem also exist for more general stochastic processes with index sets and state spaces other than the real line.
|
|
The random or stochastic error in a measurement is the error that is random from one measurement to the next. Stochastic errors tend to be normally distributed when the stochastic error is the sum of many independent random errors because of the central limit theorem. Stochastic errors added to a regression equation account for the variation in Y that cannot be explained by the included Xs.
|
|
In the LPI-procedure the decision maker linearizes any fuzziness instead of applying a membership function. This can be done by establishing stochastic and non-stochastic LPI-relations. A mixed stochastic and non- stochastic fuzzification is often a basis for the LPI-procedure. By using the LPI-methods any fuzziness in any decision situation can be considered on the base of the linear fuzzy logic.
|
|
There are several different definitions and types of stochastic matrices: :A right stochastic matrix is a real square matrix, with each row summing to 1. :A left stochastic matrix is a real square matrix, with each column summing to 1. :A doubly stochastic matrix is a square matrix of nonnegative real numbers with each row and column summing to 1. In the same vein, one may define a stochastic vector (also called probability vector) as a vector whose elements are nonnegative real numbers which sum to 1.
|
|
In numerical methods for stochastic differential equations, the Markov chain approximation method (MCAM) belongs to the several numerical (schemes) approaches used in stochastic control theory. Regrettably the simple adaptation of the deterministic schemes for matching up to stochastic models such as the Runge–Kutta method does not work at all. It is a powerful and widely usable set of ideas, due to the current infancy of stochastic control it might be even said 'insights.' for numerical and other approximations problems in stochastic processes.Harold J Kushner, Paul G Dupuis, Numerical methods for stochastic control problems in continuous time, Applications of mathematics 24, Springer-Verlag, 1992.
|
|
Fried, Shimony, Benbassat, and Wenner 2013 The directed version of the stochastic problem is known in operations research as the Stochastic Shortest Path Problem with Recourse.
|
|
Mark Damian McDonnell (born 28 February 1975) is an electronic engineer and mathematician, notable for his work on stochastic resonance and more specifically suprathreshold stochastic resonance.
|
|
In process calculus a stochastic probe is a measurement device that measures the time between arbitrary start and end events over a stochastic process algebra model.
|
|
The definition of Bayesian games has been combined with stochastic games to allow for environment states (e.g. physical world states) and stochastic transitions between states. The resulting "stochastic Bayesian game" model is solved via a recursive combination of the Bayesian Nash equilibrium and the Bellman optimality equation.
|
|
The stochastic mean of that coin-toss process is 1/2 and the drift rate of the stochastic mean is 0, assuming 1 = heads and 0 = tails.
|
|
In probability theory and statistics, a continuous-time stochastic process, or a continuous-space-time stochastic process is a stochastic process for which the index variable takes a continuous set of values, as contrasted with a discrete-time process for which the index variable takes only distinct values. An alternative terminology uses continuous parameter as being more inclusive.Parzen, E. (1962) Stochastic Processes, Holden-Day. (Chapter 6) A more restricted class of processes are the continuous stochastic processes: here the term often (but not alwaysDodge, Y. (2006) The Oxford Dictionary of Statistical Terms, OUP.
|
|
Research is underway in applying stochastic forensics to these operating systems as well as databases. Additionally, in its current state, stochastic forensics requires a trained forensic analyst to apply and evaluate. There have been calls for development of tools to automate stochastic forensics by Guidance Software and others.
|
|
"Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. Stochastic models depend on the chance variations in risk of exposure, disease and other illness dynamics.
|
|
Control Techniques for Complex Networks, Cambridge University Press, 2007. Asmussen, Søren, Glynn, Peter W., 2007. "Stochastic Simulation: Algorithms and Analysis". Springer. Series: Stochastic Modelling and Applied Probability, Vol.
|
|
Although Khinchin gave mathematical definitions of stochastic processes in the 1930s, specific stochastic processes had already been discovered in different settings, such as the Brownian motion process and the Poisson process. Some families of stochastic processes such as point processes or renewal processes have long and complex histories, stretching back centuries.
|
|
Another field that uses optimization techniques extensively is operations research. Operations research also uses stochastic modeling and simulation to support improved decision-making. Increasingly, operations research uses stochastic programming to model dynamic decisions that adapt to events; such problems can be solved with large-scale optimization and stochastic optimization methods.
|
|
Mark Herbert Ainsworth Davis (1945–2020) was Professor of Mathematics at Imperial College London. He made fundamental contributions to the theory of stochastic processes, stochastic control and mathematical finance.
|
|
In probability theory -- specifically, in stochastic analysis -- a killed process is a stochastic process that is forced to assume an undefined or "killed" state at some (possibly random) time.
|
|
Dentcheva developed the theory of Steiner selections of multifunctions, the theory of stochastic dominance constraints Higle, J. L., Stochastic programming: Optimization when uncertainty matters, Tutorials in Operations Research, INFORMS 2005, . (jointly with Andrzej Ruszczyński), and contributed to the theory of unit commitment in power systems (with Werner Römisch). Wallace, S.W.; Fleten, S.E., Stochastic Programming Models in Energy, in: Ruszczynski, A. and Shapiro, A., (eds.) (2003) Stochastic Programming. Handbooks in Operations Research and Management Science, Vol.
|
|
The first (and last) International Symposium on Stochastic Computing took place in 1978; active research in the area dwindled over the next few years. Although stochastic computing declined as a general method of computing, it has shown promise in several applications. Research has traditionally focused on certain tasks in machine learning and control. Somewhat recently, interest has turned towards stochastic decoding, which applies stochastic computing to the decoding of error correcting codes.
|
|
459-470, Aug. 2013. See the Review of Modern Physics article for a comprehensive overview of stochastic resonance. Stochastic Resonance has found noteworthy application in the field of image processing.
|
|
P E Kloeden, Eckhard Platen, Numerical Solutions of Stochastic Differential Equations, Applications of Mathematics 23, Stochastic Modelling and Applied probability, Springer, 1992. They represent counterparts from deterministic control theory such as optimal control theory.F. B. Hanson, "Markov Chain Approximation", in C. T. Leondes, ed., Stochastic Digital Control System Techniques, Academic Press, 1996, .
|
|
If the state space is the real line, then the stochastic process is referred to as a real-valued stochastic process or a process with continuous state space. If the state space is n-dimensional Euclidean space, then the stochastic process is called a n-dimensional vector process or n-vector process.
|
|
For the construction of such a stochastic process, it is assumed that the sample functions of the stochastic process belong to some suitable function space, which is usually the Skorokhod space consisting of all right- continuous functions with left limits. This approach is now more used than the separability assumption, but such a stochastic process based on this approach will be automatically separable. Although less used, the separability assumption is considered more general because every stochastic process has a separable version. It is also used when it is not possible to construct a stochastic process in a Skorokhod space.
|
|
While the basic idea behind stochastic approximation can be traced back to the Robbins–Monro algorithm of the 1950s, stochastic gradient descent has become an important optimization method in machine learning.
|
|
Jonathan Grier is a computer scientist, consultant, and entrepreneur. He is best known for his work on stochastic forensics and insider data theft.Grier, Jonathan (2011). "Detecting data theft using stochastic forensics".
|
|
An n × n matrix P is doubly stochastic precisely if both P and its transpose PT are stochastic matrices. A stochastic matrix is a square matrix of nonnegative real entries in which the sum of the entries in each column is 1. Thus, a doubly stochastic matrix is a square matrix of nonnegative real entries in which the sum of the entries in each row and the sum of the entries in each column is 1.
|
|
The tendency to stochastic defects is worse when the image consists of photons from different patterns, such as from a large-area pattern or from defocus over a large pupil fill.The Stochastic Impact of Defocus in EUV LithographyThe Stochastic Impact of Defocus in EUV Lithography Multiple failure modes may exist for the same population. For example, besides bridging of trenches, the lines separating the trenches may be broken. This can be attributed to stochastic resist loss, from secondary electrons.
|
|
A stochastic investment model tries to forecast how returns and prices on different assets or asset classes, (e. g. equities or bonds) vary over time. Stochastic models are not applied for making point estimation rather interval estimation and they use different stochastic processes. Investment models can be classified into single-asset and multi-asset models.
|
|
In mathematics of stochastic systems, the Runge–Kutta method is a technique for the approximate numerical solution of a stochastic differential equation. It is a generalisation of the Runge–Kutta method for ordinary differential equations to stochastic differential equations (SDEs). Importantly, the method does not involve knowing derivatives of the coefficient functions in the SDEs.
|
|
Jean Jacod (born 1944) is a French mathematician specializing in Stochastic processes and probability theory. He has been a professor at the Université Pierre et Marie Curie. He has made fundamental contributions to a wide range of topics in probability theory including stochastic calculus, limit theorems, martingale problems, Malliavin calculus and statistics of stochastic processes.
|
|
Ontos, 63-78.J. Glimm, D. Sharp, Stochastic Differential Equations: Selected Applications in Continuum Physics, in: R.A. Carmona, B. Rozovskii (ed.) Stochastic Partial Differential Equations: Six Perspectives, American Mathematical Society (October 1998) ().
|
|
The Stochastic Modeling of Elementary Psychological Processes.Townsend, J. T., & Ashby, F. G. (1983). The Stochastic Modeling of Elementary Psychological Processes. Cambridge: Cambridge University Press.Link, S. (1986). Wogols, Turgles and Whimpf and Things.
|
|
In this relation, Euclidean Green's functions become correlation functions in the statistical mechanical system. A statistical mechanical system in equilibrium can be modeled, via the ergodic hypothesis, as the stationary distribution of a stochastic process. Then the Euclidean path integral measure can also be thought of as the stationary distribution of a stochastic process; hence the name stochastic quantization.
|
|
Wiener or Brownian motion process on the surface of a sphere. The Wiener process is widely considered the most studied and central stochastic process in probability theory. In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables. Many stochastic processes can be represented by time series.
|
|
Stereological formulae, applications for marked point process, development of stochastic models. Successful joint work with Joseph Mecke led to the first exact proof of the fundamental stereological formulae. The book Stochastic Geometry and its Applications, by D. Stoyan, W.S. Kendall and J. Mecke reports on the results. The book of 1995 is the key reference for applied stochastic geometry.
|
|
Rotational sampling can be divided into two parts: deterministic and stochastic. Deterministic processes present themselves as spikes on a power spectrum, whereas stochastic processes are broader i.e. spread over a wider frequency range.
|
|
Graphene foams and graphite foams are examples of stochastic foams.
|
|
Nevertheless, its small range makes it vulnerable to stochastic events.
|
|
Hairer is active in the field of stochastic partial differential equations in particular, and in stochastic analysis and stochastic dynamics in general. He has worked on variants of Hörmander's theorem, systematisation of the construction of Lyapunov functions for stochastic systems, development of a general theory of ergodicity for non- Markovian systems, multiscale analysis techniques, theory of homogenisation, theory of path sampling and theory of rough paths and, in 2014, on his theory of regularity structures. Under the name HairerSoft, he develops Macintosh software.
|
|
In the mathematics of probability, a subordinator is a concept related to stochastic processes. A subordinator is itself a stochastic process of the evolution of time within another stochastic process, the subordinated stochastic process. In other words, a subordinator will determine the random number of "time steps" that occur within the subordinated process for a given unit of chronological time. In order to be a subordinator a process must be a Lévy process It also must be increasing, almost surely.
|
|
Suprathreshold stochastic resonance is a particular form of stochastic resonance. It is the phenomenon where random fluctuations, or noise, provide a signal processing benefit in a nonlinear system. Unlike most of the nonlinear systems where stochastic resonance occurs, suprathreshold stochastic resonance occurs not only when the strength of the fluctuations is small relative to that of an input signal, but occurs even for the smallest amount of random noise. Furthermore, it is not restricted to a subthreshold signal, hence the qualifier.
|
|
In stochastic analysis, the usual way to model a random process, or field, is done by specifying the dynamics of the process through a stochastic (partial) differential equation (SPDE). It is known, that solutions of (partial) differential equations can in some cases be given as an integral of a Green's function convolved with another function – if the differential equation is stochastic, i.e. contaminated by random noise (e.g. white noise) the corresponding solution would be a stochastic integral of the Green's function.
|
|
Robert Sh. Liptser (; , 20 March 1936 – 2 January 2019) was a Russian-Israeli mathematician who made contributions to the theory and applications of stochastic processes, in particular to martingales, stochastic control and nonlinear filtering.
|
|
Articles and papers in the journal describe theory, experiments, algorithms, numerical simulation and applications of stochastic phenomena, with a particular focus on random or stochastic ordinary, partial or functional differential equations and random mappings.
|
|
Stochastic Block Model have been recognised to be a topic model on bipartite networks . In a network of documents and words, Stochastic Block Model can identify topics: group of words with a similar meaning.
|
|
Added space-time noise \eta(x,t) forms a stochastic Burgers' equationW. Wang and A. J. Roberts. Diffusion approximation for self- similarity of stochastic advection in Burgers’ equation. Communications in Mathematical Physics, July 2014.
|
|
In probability theory, Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, characterize stochastic processes. In particular, they describe how the probability that a stochastic process is in a certain state changes over time.
|
|
M. Haenggi. Stochastic geometry for wireless networks. Cambridge University Press, 2012.
|
|
It is currently believed this is a form of stochastic resonance.
|
|
The concept of stationarity may be extended to two stochastic processes.
|
|
Recent experimental results have demonstrated that gene expression is a stochastic process. Thus, many authors are now using the stochastic formalism, after the work by Arkin et al. Works on single gene expression and small synthetic genetic networks, such as the genetic toggle switch of Tim Gardner and Jim Collins, provided additional experimental data on the phenotypic variability and the stochastic nature of gene expression. The first versions of stochastic models of gene expression involved only instantaneous reactions and were driven by the Gillespie algorithm.
|
|
Both jittering and stochastic undersampling degrade the representation of the TFSn more than the representation of the ENVn. Both jittering and stochastic undersampling impair the recognition of speech in noisy backgrounds without degrading recognition in silence, support the argument that TFSn is important for recognizing speech in noise. Both jittering and stochastic undersampling mimic the effects of aging on speech perception.
|
|
Stochastic Hydrology quantifies uncertainty with the aid of statistical models, used for analyzing and predicting various field scale processes. G. Dagan, "Gedeon Dagan: A Brief Story of My Life...", Ground Water, Vol. 47. No. 1, 2009, p. 164. G. Dagan, On the application of stochastic modeling of groundwater flow and transport, Contribution to Forum on The State of Stochastic Hydrology, Stoch. Envir. Res.
|
|
Together with Jean-Francois Mertens, he proved the existence of the uniform value of zero-sum undiscounted stochastic games.Mertens, J.F., and Neyman, A. (1981). "Stochastic Games," International Journal of Game Theory, 10: 53–66. This work is considered one of the most important works in the theory of stochastic games, solving a problem that had been open for over 20 years.
|
|
Malliavin introduced Malliavin calculus to provide a stochastic proof that Hörmander's condition implies the existence of a density for the solution of a stochastic differential equation; Hörmander's original proof was based on the theory of partial differential equations. His calculus enabled Malliavin to prove regularity bounds for the solution's density. The calculus has been applied to stochastic partial differential equations.
|
|
In two papers, Petters, Rider, and Teguia took first steps in creating a mathematical theory of stochastic gravitational microlensing. They characterized to several asymptotic orders the probability densities of random time delay functions, lensing maps, and shear maps in stochastic microlensing and determined a Kac- Rice type formula for the global expected number of images due to a general stochastic lens system.
|
|
Gene expression modelled as stochastic process An area that has benefited significantly from SDE is biology or more precisely mathematical biology. Here the number of publications on the use of stochastic model grew, as most of the models are nonlinear, demanding numerical schemes. The graphic depicts a stochastic differential equation being solved using the Euler Scheme. The deterministic counterpart is shown as well.
|
|
Two modes of learning are available: stochastic and batch. In stochastic learning, each input creates a weight adjustment. In batch learning weights are adjusted based on a batch of inputs, accumulating errors over the batch. Stochastic learning introduces "noise" into the process, using the local gradient calculated from one data point; this reduces the chance of the network getting stuck in local minima.
|
|
Originally introduced by Richard E. Bellman in , stochastic dynamic programming is a technique for modelling and solving problems of decision making under uncertainty. Closely related to stochastic programming and dynamic programming, stochastic dynamic programming represents the problem under scrutiny in the form of a Bellman equation. The aim is to compute a policy prescribing how to act optimally in the face of uncertainty.
|
|
The stochastic version, where each edge is associated with a probability of independently being in the graph, has been given considerable attention in operations research under the name "the Stochastic Shortest Path Problem with Recourse" (SSPPR).
|
|
Drawing on this, stochastic mechanics has been used to successfully investigate insider data theft where other techniques have failed. Typically, after stochastic forensics has identified the data theft, follow up using traditional forensic techniques is required.
|
|
Although stochastic computing was a historical failure, it may still remain relevant for solving certain problems. To understand when it remains relevant, it is useful to compare stochastic computing with more traditional methods of digital computing.
|
|
These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries. The term random function is also used to refer to a stochastic or random process, because a stochastic process can also be interpreted as a random element in a function space. The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. But often these two terms are used when the random variables are indexed by the integers or an interval of the real line.
|
|
He also consulted with the development of professional stochastic-optimization software (IBM).
|
|
A Markov decision process is a stochastic game with only one player.
|
|
In this case, the scheduling problems are referred to as Stochastic scheduling.
|
|
It is known that a stochastic version of the standard (deterministic) Newton-Raphson algorithm (a “second-order” method) provides an asymptotically optimal or near-optimal form of stochastic approximation. SPSA can also be used to efficiently estimate the Hessian matrix of the loss function based on either noisy loss measurements or noisy gradient measurements (stochastic gradients). As with the basic SPSA method, only a small fixed number of loss measurements or gradient measurements are needed at each iteration, regardless of the problem dimension p. See the brief discussion in Stochastic gradient descent.
|
|
When the index set T can be interpreted as time, a stochastic process is said to be stationary if its finite-dimensional distributions are invariant under translations of time. This type of stochastic process can be used to describe a physical system that is in steady state, but still experiences random fluctuations. The intuition behind stationarity is that as time passes the distribution of the stationary stochastic process remains the same. A sequence of random variables forms a stationary stochastic process only if the random variables are identically distributed.
|
|
Stochastic scheduling concerns scheduling problems involving random attributes, such as random processing times, random due dates, random weights, and stochastic machine breakdowns. Major applications arise in manufacturing systems, computer systems, communication systems, logistics and transportation, machine learning, etc.
|
|
1, pp. 1–149, 2006. The drift-plus-penalty method can also be used to minimize the time average of a stochastic process subject to time average constraints on a collection of other stochastic processes. M. J. Neely.
|
|
If the first order stochastic dominance constraint is employed, the utility function u(x) is nondecreasing; if the second order stochastic dominance constraint is used, u(x) is nondecreasing and concave. A system of linear equations can test whether a given solution if efficient for any such utility function. Third-order stochastic dominance constraints can be dealt with using convex quadratically constrained programming (QCP).
|
|
Nicole El Karoui's research is focused on probability theory, stochastic control theory and mathematical finance. Her contributions focused on the mathematical theory of stochastic control, backward stochastic differential equations and their application in mathematical finance. She is particularly known for her work on the robustness of the Black-Scholes hedging strategy, superhedging of contingent claims and the change of numéraire method for option pricing.
|
|
In mathematical finance, the stochastic volatility jump (SVJ) model is suggested by Bates.David S. Bates, "Jumps and Stochastic volatility: Exchange Rate Processes Implicity in Deutsche Mark Options", The Review of Financial Studies, volume 9, number 1, 1996, pages 69–107. This model fits the observed implied volatility surface well. The model is a Heston process for stochastic volatility with an added Merton log-normal jump.
|
|
American Mathematical Soc. pp. 464–466. . Stochastic matrices were further developed by scholars like Andrey Kolmogorov, who expanded their possibilities by allowing for continuous-time Markov processes. By the 1950s, articles using stochastic matrices had appeared in the fields of econometrics and circuit theory. In the 1960s, stochastic matrices appeared in an even wider variety of scientific works, from behavioral science to geology to residential planning.
|
|
In stochastic calculus, the Doléans-Dade exponential, Doléans exponential, or stochastic exponential, of a semimartingale X is defined to be the solution to the stochastic differential equation with initial condition . The concept is named after Catherine Doléans-Dade. It is sometimes denoted by Ɛ(X). In the case where X is differentiable, then Y is given by the differential equation to which the solution is .
|
|
Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations. They have relevance to quantum field theory, statistical mechanics, and spatial modeling.
|
|
Sudoku can be solved using stochastic (random-based) algorithms.Lewis, R (2007) Metaheuristics Can Solve Sudoku Puzzles Journal of Heuristics, vol. 13 (4), pp 387-401.Perez, Meir and Marwala, Tshilidzi (2008) Stochastic Optimization Approaches for Solving Sudoku arXiv:0805.0697.
|
|
K. David Elworthy Kenneth David Elworthy is a Professor Emeritus of Mathematics at the University of Warwick.People at the Mathematics Institute, Univ. of Warwick, retrieved 2011-05-02. He works on stochastic analysis, stochastic differential equations and geometric analysis.
|
|
The parameter \mu represents the risk-neutral drift of the underlying stochastic process.
|
|
Another stochastic gradient descent algorithm is the least mean squares (LMS) adaptive filter.
|
|
Stochastic problems in physics and astronomy. Reviews of modern physics, 15(1), 1.
|
|
Stochastic Models For Bacteriophage. Methuen & Co. Ltd., London. OCLC 279694 #Hayes, W., 1964.
|
|
M. Haenggi. Stochastic geometry for wireless networks. Chapter 2. Cambridge University Press, 2012.
|
|
The wake-sleep algorithm is convergent and can be stochastic if alternated appropriately.
|
|
The terms "narratives of insecurity", "scripted violence" and "stochastic terrorism" are linked in an indirect chain cause–effect relationship. Public use of "narratives of insecurity" can prompt the rhetoric of "scripted violence" which can result in an act of "stochastic terrorism".
|
|
The motion of a particle is described by the Smoluchowski limit of the Langevin equation:Z. Schuss, Theory and Applications of Stochastic Differential Equations (Wiley Series in Probability and Statistics - (1980)Z. Schuss, Theory and Applications of Stochastic Processes. An Analytical Approach.
|
|
In mathematical statistics, growth curves such as those used in biology are often modeled as being continuous stochastic processes, e.g. as being sample paths that almost surely solve stochastic differential equations. Growth curves have been also applied in forecasting market development.
|
|
In graph theory, a fractional isomorphism of graphs whose adjacency matrices are denoted A and B is a doubly stochastic matrix D such that DA = BD. If the doubly stochastic matrix is a permutation matrix, then it constitutes a graph isomorphism.
|
|
In the case where the conditioned system state is always pure, the unraveling could be in the form of a stochastic Schrödinger equation (SSE). If the state may become mixed, then it is necessary to use a stochastic master equation (SME).
|
|
Stochastic computing is a collection of techniques that represent continuous values by streams of random bits. Complex computations can then be computed by simple bit-wise operations on the streams. Stochastic computing is distinct from the study of randomized algorithms.
|
|
Gardner provided the original definition and mathematical characterization of almost cyclostationary (ACS) stochastic processes, including poly-CS stochastic processes. He further gave the original definition and mathematical characterization of non-stochastic fraction-of-time (FOT) probabilistic models of CS, ACS, and poly-CS time-series. He also originated the extensions and generalizations of the core theorems and relations comprising the second order and higher-order theories of stationary stochastic processes and stationary non-stochastic time-series to CS, poly-CS, and ACS processes and times-series. In 1987, Professor Gardner was invited by the Editor of IEEE Signal Processing Magazine to write an introduction, for the signal processing community, to the recently discovered 1914 contribution of Albert Einstein to time-series analysis.
|
|
In mathematics and telecommunications, stochastic geometry models of wireless networks refer to mathematical models based on stochastic geometry that are designed to represent aspects of wireless networks. The related research consists of analyzing these models with the aim of better understanding wireless communication networks in order to predict and control various network performance metrics. The models require using techniques from stochastic geometry and related fields including point processes, spatial statistics, geometric probability, percolation theory, as well as methods from more general mathematical disciplines such as geometry, probability theory, stochastic processes, queueing theory, information theory, and Fourier analysis.F. Baccelli and B. Błaszczyszyn. Stochastic Geometry and Wireless Networks, Volume I — Theory, volume 3, No 3–4 of Foundations and Trends in Networking.
|
|
Neyman, A. (2017), "Continuous-Time Stochastic Games," Games and Economic Behaviour, 104, pp. 92-130. He also co-edited, together with Sylvain Sorin, a comprehensive collection of works in the field of stochastic games.Nato Science Series: Mathematical and Physical Sciences, Volume 570, Proceedings of the NATO Advanced Study Institute on Stochastic Games and Applications (Neyman, A. and Sorin, S. (eds)), held in Stony Brook, NY during July 7–17, 1999.
|
|
Stochastic integrals can rarely be solved in analytic form, making stochastic numerical integration an important topic in all uses of stochastic integrals. Various numerical approximations converge to the Stratonovich integral, and variations of these are used to solve Stratonovich SDEs . Note however that the most widely used Euler scheme (the Euler–Maruyama method) for the numeric solution of Langevin equations requires the equation to be in Itô form.
|
|
Differential games have been applied to economics. Recent developments include adding stochasticity to differential games and the derivation of the stochastic feedback Nash equilibrium (SFNE). A recent example is the stochastic differential game of capitalism by Leong and Huang (2010). In 2016 Yuliy Sannikov received the Clark Medal from the American Economic Association for his contributions to the analysis of continuous time dynamic games using stochastic calculus methods.
|
|
Stochastic printing of sub-resolution assist features. SRAFs receive low enough doses which are close enough to printing that they will have more significant stochastic impact on printing. Here the SRAF printing error occurs at the far right. As SRAFs are smaller features than primary features and are not supposed to receive doses high enough to print, they are more susceptible to stochastic dose variations causing printing errors.
|
|
400x400px A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Scholes model.
|
|
I realized that stochasticity had its limits; there was something else at play in the universe. That realization forced a major alteration of my Stochastic Space-time theory, a modification I call Crypto-stochastic Spacetime theory.” Almost immediately, Crypto- stochastic Space-time theory gave results: he could explain the two-slit experiment, superposition in general, and explain photon polarization (a more compelling explanation than afforded by conventional quantum mechanics).
|
|
Moshe Shaked was a Fellow of the Institute of Mathematical Statistics. Shaked was a leading figure in stochastic order and distribution theory. He published widely in applied probability and statistics. He became most celebrated internationally for his collection of influential papers on stochastic order and multivariate dependence. Shaked’s contribution also includes pioneering studies on stochastic convexity and on multivariate phase-type distributions, with important applications in reliability modelling and queueing analysis.
|
|
No industry-standard models yet exist that have stochastic correlation and are arbitrage-free.
|
|
If two stochastic processes X and Y are independent, then they are also uncorrelated.
|
|
The stochastic terrorist in this context does not direct the actions of any particular individual or members of a group. Rather, the stochastic terrorist gives voice to a specific ideology via mass media with the aim of optimizing its dissemination. It is by dint of this ideology that the stochastic terrorist is alleged to randomly incite individuals predisposed to acts of violence. And it is because the stochastic terrorist does not target and incite individual perpetrators of terror with their message that the perpetrator may be labeled a lone wolf by law enforcement while the inciter avoids legal culpability.
|
|
Instead, stochastic approximation algorithms use random samples of F(\theta,\xi) to efficiently approximate properties of f such as zeros or extrema. Recently, stochastic approximations have found extensive applications in the fields of statistics and machine learning, especially in settings with big data. These applications range from stochastic optimization methods and algorithms, to online forms of the EM algorithm, reinforcement learning via temporal differences, and deep learning, and others. Stochastic approximation algorithms have also been used in the social sciences to describe collective dynamics: fictitious play in learning theory and consensus algorithms can be studied using their theory.
|
|
The first relatively coherent stochastic theory of quantum mechanics was put forward by Hungarian physicist Imre FényesSee who was able to show the Schrödinger equation could be understood as a kind of diffusion equation for a Markov process. Louis de Broglie felt compelled to incorporate a stochastic process underlying quantum mechanics to make particles switch from one pilot wave to another. Perhaps the most widely known theory where quantum mechanics is assumed to describe an inherently stochastic process was put forward by Edward NelsonSee and is called stochastic mechanics. This was also developed by Davidson, Guerra, Ruggiero and others.
|
|
The printing of both the text and the image pages used stochastic lithography in order to create outstanding quality prints from the original watercolours. Stochastic lithography is an advancement in printing technology that can give a better print quality, cleaner more dynamic and accurate colour images, and reduce running waste. Whereas conventional lithography uses half-tone dots of various sizes and spaces these dots at the same distance from each other, stochastic lithography uses microdots of a common size of various spacing according to tonal value. Stochastic screening uses smaller printing dots to create a higher image detail.
|
|
In a continuous time approach in a finance context, the state variable in the stochastic differential equation is usually wealth or net worth, and the controls are the shares placed at each time in the various assets. Given the asset allocation chosen at any time, the determinants of the change in wealth are usually the stochastic returns to assets and the interest rate on the risk-free asset. The field of stochastic control has developed greatly since the 1970s, particularly in its applications to finance. Robert Merton used stochastic control to study optimal portfolios of safe and risky assets.
|
|
Moreover, the underlying operations in a digital multiplier are full adders, whereas a stochastic computer only requires an AND gate. Additionally, a digital multiplier would naively require 2n input wires, whereas a stochastic multiplier would only require 2 input wires. (If the digital multiplier serialized its output, however, it would also require only 2 input wires.) Additionally, stochastic computing is robust against noise; if a few bits in a stream are flipped, those errors will have no significant impact on the solution. Furthermore, stochastic computing elements can tolerate skew in the arrival time of the inputs.
|
|
In probability theory, the Skorokhod problem is the problem of solving a stochastic differential equation with a reflecting boundary condition. The problem is named after Anatoliy Skorokhod who first published the solution to a stochastic differential equation for a reflecting Brownian motion.
|
|
Later in his career, he worked on stochastic processes, stochastic differential equations and their applications in control theory. In 1976–1977 he was a Guggenheim Fellow. In 1982 he gave a plenary address (Optimal control of Markov Processes) at the ICM in Warsaw.
|
|
SDEs frequently occur in physics in Stratonovich form, as limits of stochastic differential equations driven by colored noise if the correlation time of the noise term approaches zero. For a recent treatment of different interpretations of stochastic differential equations see for example .
|
|
Unfortunately, generating (pseudo-)random bits is fairly costly (compared to the expense of, e.g., a full adder). Therefore, the gate-level advantage of stochastic computing is typically lost. Third, the analysis of stochastic computing assumes that the bit streams are independent (uncorrelated).
|
|
In mathematics, a Bessel process, named after Friedrich Bessel, is a type of stochastic process.
|
|
In 2012, Cambridge University Press published one of his books, Stochastic Geometry for Wireless Networks.
|
|
Zhang’s current research interests are system identification, adaptive control, stochastic systems, and multi-agent systems.
|
|
In fact, the exact recovery threshold is known for the fully general stochastic block model.
|
|
The increased secondary electron blur with increased dose makes control of stochastic defects more difficult.
|
|
A discrete-time stochastic process satisfying the Markov property is known as a Markov chain.
|
|
Zabinsky is the author of the book Stochastic Adaptive Search in Global Optimization (Kluwer, 2004).
|
|
The term has mostly been applied to domestic American incidents of violence. In their 2017 book Age of Lone Wolf Terrorism, criminologist Mark S. Hamm and sociologist Ramón Spaaij discuss stochastic terrorism as a form of "indirect enabling" of terrorists. They write that "stochastic terrorism is the method of international recruitment used by ISIS", and they refer to Anwar al-Awlaki and Alex Jones as stochastic terrorists. Hamm and Spaaij discuss two instances of violence.
|
|
The other commonly used type of stochastic dominance is second-order stochastic dominance. Roughly speaking, for two gambles A and B, gamble A has second-order stochastic dominance over gamble B if the former is more predictable (i.e. involves less risk) and has at least as high a mean. All risk-averse expected-utility maximizers (that is, those with increasing and concave utility functions) prefer a second-order stochastically dominant gamble to a dominated one.
|
|
World War II greatly interrupted the development of probability theory, causing, for example, the migration of Feller from Sweden to the United States of America and the death of Doeblin, considered now a pioneer in stochastic processes. Mathematician Joseph Doob did early work on the theory of stochastic processes, making fundamental contributions, particularly in the theory of martingales. His book Stochastic Processes is considered highly influential in the field of probability theory.
|
|
However, a stochastic process is by nature continuous while a time series is a set of observations indexed by integers. A stochastic process may involve several related random variables. Common examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner.
|
|
Stochastic Cellular Automata are CA whose updating rule is a stochastic one, which means the new entities' states are chosen according to some probability distributions. It is a discrete-time random dynamical system. From the spatial interaction between the entities, despite the simplicity of the updating rules, complex behaviour may emerge like self-organization. As mathematical object, it may be considered in the framework of stochastic processes as an interacting particle system in discrete-time.
|
|
In addition, much mathematical work was also done through these decades to improve the range of uses and functionality of the stochastic matrix and Markovian processes more generally. From the 1970s to present, stochastic matrices have found use in almost every field that requires formal analysis, from structural science to medical diagnosis to personnel management. In addition, stochastic matrices have found wide use in land change modeling, usually under the term Markov matrix.
|
|
An alternative view on SDEs is the stochastic flow of diffeomorphisms. This understanding is unambiguous and corresponds to the Stratonovich version of the continuous time limit of stochastic difference equations. Associated with SDEs is the Smoluchowski equation or the Fokker–Planck equation, an equation describing the time evolution of probability distribution functions. The generalization of the Fokker–Planck evolution to temporal evolution of differential forms is provided by the concept of stochastic evolution operator.
|
|
Brownian motion or the Wiener process was discovered to be exceptionally complex mathematically. The Wiener process is almost surely nowhere differentiable; thus, it requires its own rules of calculus. There are two dominating versions of stochastic calculus, the Itô stochastic calculus and the Stratonovich stochastic calculus. Each of the two has advantages and disadvantages, and newcomers are often confused whether the one is more appropriate than the other in a given situation.
|
|
A significant extension of the CIR model to the case of stochastic mean and stochastic volatility is given by Lin Chen (1996) and is known as Chen model. A more recent extension is the so-called CIR # by Orlando, Mininni and Bufalo (2018, 2019 , ).
|
|
Since the late 20th century it became more popular to consider a Markov chain as a stochastic process with discrete index set, living on a measurable state space.Sean Meyn and Richard L. Tweedie: Markov Chains and Stochastic Stability. 2nd edition, 2009.Daniel Revuz: Markov Chains.
|
|
Spatial point processes and their applications. Stochastic Geometry: Lectures given at the CIME Summer School held in Martina Franca, Italy, September 13–18, 2004, pages 1-75, 2007. as well as the related fields of stochastic geometry and spatial statisticsJ. Moller and R. P. Waagepetersen.
|
|
Nigel Geoffrey Stocks (born 6 September 1964) is an engineer and physicist, notable for discovering suprathreshold stochastic resonance (SSR) and its application to cochlear implant technology.Mark D. McDonnell, Nigel G. Stocks, Charles E. M. Pearce, and Derek Abbott, Stochastic Resonance, Cambridge University Press, 2008.
|
|
In the following subsections we discuss versions of Itô's lemma for different types of stochastic processes.
|
|
The following examples give explicit expressions for the Onsager–Machlup function of a continuous stochastic processes.
|
|
The Zakai equation is a bilinear stochastic partial differential equation. It was named after Moshe Zakai.
|
|
The latter makes it susceptible to stochastic events. In addition, climate change is a potential threat.
|
|
One approach for avoiding mathematical construction issues of stochastic processes, proposed by Joseph Doob, is to assume that the stochastic process is separable. Separability ensures that infinite-dimensional distributions determine the properties of sample functions by requiring that sample functions are essentially determined by their values on a dense countable set of points in the index set. Furthermore, if a stochastic process is separable, then functionals of an uncountable number of points of the index set are measurable and their probabilities can be studied. Another approach is possible, originally developed by Anatoliy Skorokhod and Andrei Kolmogorov, for a continuous-time stochastic process with any metric space as its state space.
|
|
Defocus incurs different phase differences (shown here as different colors) between interfering beams from different pupil points, leading to different images. Photons from different points must therefore be divided among at least several groups, reducing their numbers and increasing stochastic effects. Photon division among diffraction patterns in the pupil. Stochastic effects are aggravated by the division of photons into fewer numbers per diffraction pattern (each represented here as a different color with different % of photons within the pupil quadrant) across the pupil.The Stochastic Variation of EUV Source IlluminationApplication-Specific Lithography: a 28 nm Pitch DRAM Active Area Stochastic defects arise from dose-dependent blur.
|
|
Longitudinal studies of secular events are frequently conceptualized as consisting of a trend component fitted by a polynomial, a cyclical component often fitted by an analysis based on autocorrelations or on a Fourier series, and a random component (stochastic drift) to be removed. In the course of the time series analysis, identification of cyclical and stochastic drift components is often attempted by alternating autocorrelation analysis and differencing of the trend. Autocorrelation analysis helps to identify the correct phase of the fitted model while the successive differencing transforms the stochastic drift component into white noise. Stochastic drift can also occur in population genetics where it is known as genetic drift.
|
|
SGLD can be applied to the optimization of non-convex objective functions, shown here to be a sum of Gaussians. Stochastic gradient Langevin dynamics (SGLD), is an optimization technique composed of characteristics from Stochastic gradient descent, a Robbins–Monro optimization algorithm, and Langevin dynamics, a mathematical extension of molecular dynamics models. Like stochastic gradient descent, SGLD is an iterative optimization algorithm which introduces additional noise to the stochastic gradient estimator used in SGD to optimize a differentiable objective function. Unlike traditional SGD, SGLD can be used for Bayesian learning, since the method produces samples from a posterior distribution of parameters based on available data.
|
|
The RASCEL stochastic computer, circa 1969 Stochastic computing was first introduced in a pioneering paper by John von Neumann in 1953. However, the theory could not be fully developed until advances in computing of the 1960s, mostly through a series of simultaneous and parallel efforts in the US and the UK. By the late 1960s, attention turned to the design of special-purpose hardware to perform stochastic computation. A host of these machines were constructed between 1969 and 1974; RASCEL is pictured in this article. Despite the intense interest in the 1960s and 1970s, stochastic computing ultimately failed to compete with more traditional digital logic, for reasons outlined below.
|
|
In quantum probability, the Belavkin equation, also known as Belavkin- Schrödinger equation, quantum filtering equation, stochastic master equation, is a quantum stochastic differential equation describing the dynamics of a quantum system undergoing observation in continuous time. It was derived and henceforth studied by Viacheslav Belavkin in 1988.
|
|
If such a Hamiltonian has a unique lowest energy state with a positive real wave-function, as it often does for physical reasons, it is connected to a stochastic system in imaginary time. This relationship between stochastic systems and quantum systems sheds much light on supersymmetry.
|
|
NoW Publishers, 2009.F. Baccelli and B. Błaszczyszyn. Stochastic Geometry and Wireless Networks, Volume II — Applications, volume 4, No 1–2 of Foundations and Trends in Networking. NoW Publishers, 2009.W. S. Kendall and I. Molchanov, eds. New Perspectives in Stochastic Geometry. Oxford University Press, 2010.
|
|
Jacobus (Jaap) Wessels (January 19, 1939 – July 30, 2009) was a Dutch mathematician and Professor of Stochastic Operations Research at the Eindhoven University of Technology.,Jo van Nunen and Jaap van der Wal. "Jaap wessels–his life with stochastic processes." Statistica Neerlandica 54.2 (2000): 116-126.
|
|
The primary objective for scheduling actions having TUFs is maximal utility accrual (UA). The accrued utility is an application-specific polynomial sum of the schedule's completed actions' utilities. When actions have one or more stochastic parameters (e.g., operation duration), the accrued utility is also stochastic (i.e.
|
|
A simple iterative method to approach the double stochastic matrix is to alternately rescale all rows and all columns of A to sum to 1. Sinkhorn and Knopp presented this algorithm and analyzed its convergence. Sinkhorn, Richard, & Knopp, Paul. (1967). "Concerning nonnegative matrices and doubly stochastic matrices".
|
|
Cointegration has become an important property in contemporary time series analysis. Time series often have trends—either deterministic or stochastic. In an influential paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends.
|
|
Data Networks, Prentice Hall, published in 1988, with second edition 1992, co-authored with Dimitri Bertsekas, helped provide a conceptual foundation for this field. In the 1990s, Gallager's interests shifted back to information theory and to stochastic processes. He wrote the 1996 textbook, Discrete Stochastic Processes.
|
|
A model can be simulated using many physical assumptions: deterministic, stochastic or hybrid deterministic/stochastic; non-spatial compartmental, simulating only reaction kinetics, or with explicit spatial geometries accounting also for diffusion and flow. A new experimental feature allows for reaction-diffusion models in changing geometries (top).
|
|
If a continuous-time real-valued stochastic process meets certain moment conditions on its increments, then the Kolmogorov continuity theorem says that there exists a modification of this process that has continuous sample paths with probability one, so the stochastic process has a continuous modification or version. The theorem can also be generalized to random fields so the index set is n-dimensional Euclidean space as well as to stochastic processes with metric spaces as their state spaces.
|
|
Skorokhod function spaces are frequently used in the theory of stochastic processes because it often assumed that the sample functions of continuous-time stochastic processes belong to a Skorokhod space. Such spaces contain continuous functions, which correspond to sample functions of the Wiener process. But the space also has functions with discontinuities, which means that the sample functions of stochastic processes with jumps, such as the Poisson process (on the real line), are also members of this space.
|
|
In 1992, he was appointed as an adjunct professor at the Norwegian School of Economics and Business Administration, Bergen, Norway. His main field of interest is stochastic analysis, including stochastic control, optimal stopping, stochastic ordinary and partial differential equations and applications, particularly to physics, biology and finance. For his contributions to these fields, he was awarded the Nansen Prize in 1996. He has been a member of the Norwegian Academy of Science and Letters since 1996.
|
|
After World War II the study of probability theory and stochastic processes gained more attention from mathematicians, with significant contributions made in many areas of probability and mathematics as well as the creation of new areas. Starting in the 1940s, Kiyosi Itô published papers developing the field of stochastic calculus, which involves stochastic integrals and stochastic differential equations based on the Wiener or Brownian motion process. Also starting in the 1940s, connections were made between stochastic processes, particularly martingales, and the mathematical field of potential theory, with early ideas by Shizuo Kakutani and then later work by Joseph Doob. Further work, considered pioneering, was done by Gilbert Hunt in the 1950s, connecting Markov processes and potential theory, which had a significant effect on the theory of Lévy processes and led to more interest in studying Markov processes with methods developed by Itô.
|
|
With Zhan, Makarov published research on the stochastic properties of iterated polynomial maps (theory of Julia sets).
|
|
Notice that the rows of P sum to 1: this is because P is a stochastic matrix.
|
|
Together with Nicolas Victoir, he wrote the book Multidimensional Stochastic Processes as Rough Paths: Theory and Applications.
|
|
In probability theory, moment closure is an approximation method used to estimate moments of a stochastic process.
|
|
Stochastic FSTs (also known as probabilistic FSTs or statistical FSTs) are presumably a form of weighted FST.
|
|
Prasetio, Y. (2005). Simulation-based optimization for complex stochastic systems. University of Washington.Deng, G., & Ferris, Michael. (2007).
|
|
In probability theory, a McKean–Vlasov process is a stochastic process described by a stochastic differential equation where the coefficients of the diffusion depend on the distribution of the solution itself. The equations are a model for Vlasov equation and were first studied by Henry McKean in 1966.
|
|
We may also define functions on discontinuous stochastic processes. Let be the jump intensity. The Poisson process model for jumps is that the probability of one jump in the interval is plus higher order terms. could be a constant, a deterministic function of time, or a stochastic process.
|
|
Walter Murray Wonham (b. 1934) is a Canadian control theorist and professor at the University of Toronto. He dealt with multi-variable geometric control theory, stochastic control and stochastic filters, and more recently the control of discrete event systems from the standpoint of mathematical logic and formal languages.
|
|
Jan Hemelrijk (28 May 1918 – 16 March 2005) was a Dutch mathematician, Professor of Statistics at the University of Amsterdam, and authority in the field of stochastic processes.Jo van Nunen and Jaap van der Wal. "Jaap wessels–his life with stochastic processes." Statistica Neerlandica 54.2 (2000): 116-126.
|
|
In stochastic analysis, a part of the mathematical theory of probability, a predictable process is a stochastic process whose value is knowable at a prior time. The predictable processes form the smallest class that is closed under taking limits of sequences and contains all adapted left-continuous processes.
|
|
In probability theory, a stable process is a type of stochastic process. It includes stochastic processes whose associated probability distributions are stable distributions. Examples of stable processes include the Wiener process, or Brownian motion, whose associated probability distribution is the normal distribution. They also include the Cauchy process.
|
|
Prominent examples of stochastic algorithms are Markov chains and various uses of Gaussian distributions. Stochastic algorithms are often used together with other algorithms in various decision- making processes. Music has also been composed through natural phenomena. These chaotic models create compositions from the harmonic and inharmonic phenomena of nature.
|
|
The definition of Markov chains has evolved during the 20th century. In 1953 the term Markov chain was used for stochastic processes with discrete or continuous index set, living on a countable or finite state space, see Doob.Joseph L. Doob: Stochastic Processes. New York: John Wiley & Sons, 1953.
|
|
A, Math. Gen. 35 7187-7204: A sufficient criterion for integrability of stochastic many-body dynamics. with Brownian motion and macro effects such as object resonanceJan A. Freund (Humboldt-University, Germany) et al., ORAL session C32, 2006-03-12, Washington: Stochastic Resonance and Noise-Induced Phase Synchronization and deformation.
|
|
In this view, randomness is the opposite of determinism in a stochastic process. Hence if a stochastic system has entropy zero it has no randomness and any increase in entropy increases randomness. Shannon's formulation defaults to Boltzmann's 19th century formulation of entropy in case all probabilities are equal.
|
|
Stochastic Processes and Their Applications is a monthly peer-reviewed scientific journal published by Elsevier for the Bernoulli Society for Mathematical Statistics and Probability. The editor-in-chief is Sylvie Méléard. The principal focus of this journal is theory and applications of stochastic processes. It was established in 1973.
|
|
RBEs can be used for either cancer/hereditary risks (stochastic) or for harmful tissue reactions (deterministic) effects. Tissues have different RBEs depending on the type of effect. For high LET radiation (i.e., alphas and neutrons), the RBEs for deterministic effects tend to be lower than those for stochastic effects.
|
|
Biological processes at the molecular scale are inherently stochastic. They emerge from a combination of stochastic events that happen given the physico-chemical properties of molecules. For instance, gene expression is intrinsically noisy. This means that two cells in exactly identical regulatory states will exhibit different mRNA contents.
|
|
This represents an exponential increase in work. In certain applications, however, the progressive precision property of stochastic computing can be exploited to compensate this exponential loss. Second, stochastic computing requires a method of generating random biased bit streams. In practice, these streams are generated with pseudo-random number generators.
|
|
Ruszczyński developed decomposition methods for stochastic programming problems, the theory of stochastic dominance constraints (jointly with Darinka Dentcheva), contributed to the theory of coherent, conditional, and dynamic risk measures (jointly with Alexander Shapiro), and created the theory of Markov risk measures. Higle, J. L., Stochastic programming: Optimization when uncertainty matters, Tutorials in Operations Research, INFORMS 2005, . Rockafellar, R. T., Coherent approaches to risk in optimization under uncertainty, Tutorials in Operations Research, INFORMS 2007, . Sagastizabal, C., Divide to conquer: decomposition methods for energy optimization.
|
|
In 1953 Doob published his book Stochastic processes, which had a strong influence on the theory of stochastic processes and stressed the importance of measure theory in probability. Doob also chiefly developed the theory of martingales, with later substantial contributions by Paul-André Meyer. Earlier work had been carried out by Sergei Bernstein, Paul Lévy and Jean Ville, the latter adopting the term martingale for the stochastic process. Methods from the theory of martingales became popular for solving various probability problems.
|
|
A sample path of an Itō process together with its surface of local times. In the mathematical theory of stochastic processes, local time is a stochastic process associated with semimartingale processes such as Brownian motion, that characterizes the amount of time a particle has spent at a given level. Local time appears in various stochastic integration formulas, such as Tanaka's formula, if the integrand is not sufficiently smooth. It is also studied in statistical mechanics in the context of random fields.
|
|
Some effects of ionizing radiation on human health are stochastic, meaning that their probability of occurrence increases with dose, while the severity is independent of dose. Radiation- induced cancer, teratogenesis, cognitive decline, and heart disease are all examples of stochastic effects. Its most common impact is the stochastic induction of cancer with a latent period of years or decades after exposure. The mechanism by which this occurs is well understood, but quantitative models predicting the level of risk remain controversial.
|
|
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as unstable stock prices or physical systems subject to thermal fluctuations. Typically, SDEs contain a variable which represents random white noise calculated as the derivative of Brownian motion or the Wiener process. However, other types of random behaviour are possible, such as jump processes.
|
|
Sergey M. Bezrukov is a Russian born biophysicist notable for his work on ion channels and stochastic resonance.
|
|
Bentley, R. A. & Shennan, S. J. (2003) Cultural transmission and stochastic network growth. American Antiquity 68:459 – 85.
|
|
Neyman has made numerous contributions to game theory, including to stochastic games, the Shapley value, and repeated games.
|
|
This observation helps to explain why the Rayleigh fading assumption is frequently made when constructing stochastic geometry models.
|
|
Recently an improved and faster approach of this kind was proposed the so-called Stochastic Reconfiguration (SR) method.
|
|
They find common application in probability and stochastic processes, and in certain branches of analysis including potential theory.
|
|
Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method. Applied Mathematical Finance. Forthcoming 2016.
|
|
This is one of the simplest examples of a non-trivial capacity result for a non-stochastic channel.
|
|
Then he used these theorems to give rigorous proofs of theorems proven by Fisher and Hotelling related to Fisher's maximum likelihood estimator for estimating a parameter of a distribution. After writing a series of papers on the foundations of probability and stochastic processes including martingales, Markov processes, and stationary processes, Doob realized that there was a real need for a book showing what is known about the various types of stochastic processes, so he wrote the book Stochastic Processes.Doob J.L., Stochastic Processes It was published in 1953 and soon became one of the most influential books in the development of modern probability theory. Beyond this book, Doob is best known for his work on martingales and probabilistic potential theory.
|
|
Fluctuation-enhanced sensing (FES) is a specific type of chemical or biological sensing where the stochastic component, noise, of the sensor signal is analyzed. The stages following the sensor in a FES system typically contain filters and preamplifier(s) to extract and amplify the stochastic signal components, which are usually microscopic temporal fluctuations that are orders of magnitude weaker than the sensor signal. Then selected statistical properties of the amplified noise are analyzed, and a corresponding pattern is generated as the stochastic fingerprint of the sensed agent. Often the power density spectrum of the stochastic signal is used as output pattern however FES has been proven effective with more advanced methods, too, such as higher- order statistics.
|
|
The existence of these two phases F and S at the same flow rate does not result from the stochastic nature of traffic: Even if there were no stochastic processes in vehicular traffic, the states F and S do exist at the same flow rate. However, classical stochastic approaches to traffic control do not assume a possibility of an F→S phase transition in metastable free flow. For this reason, these stochastic approaches cannot resolve the problem of the inconsistence of classical theories with the nucleation nature of real traffic breakdown. According to Kerner, this inconsistence can explain why network optimization and control approaches based on these fundamentals and methodologies have failed by their applications in the real world.
|
|
Itô (right) with Issei Shiraishi in 1935. Shiraishi later became a mathematician. Itô pioneered the theory of stochastic integration and stochastic differential equations, now known as Itô calculus. Its basic concept is the Itô integral, and among the most important results is a change of variable formula known as Itô's lemma.
|
|
One of the most studied SPDEs is the stochastic heat equation, which may formally be written as : \partial_t u = \Delta u + \xi\;, where \Delta is the Laplacian and \xi denotes space-time white noise. Other examples also include stochastic versions of famous linear equations, such as wave equation and Schrödinger equation.
|
|
"Fast full waveform inversion with random shot decimation". SEG Technical Program Expanded Abstracts, 2011. 2804-2808 Stochastic gradient descent competes with the L-BFGS algorithm, which is also widely used. Stochastic gradient descent has been used since at least 1960 for training linear regression models, originally under the name ADALINE.
|
|
The relative abundance of each isotopologue (e.g. mass-47 CO2) is proportional to the relative abundance of each isotopic species. : This predicted abundance assumes a non-biased stochastic distribution of isotopes, natural materials tend to deviate from these stochastic values, the study of which forms the basis of clumped isotope geochemistry.
|
|
Maglaras served in various roles at the Columbia University Data Science Institute. His research focuses on stochastic modeling and data science, with an emphasis on stochastic networks, financial engineering, and quantitative pricing and revenue management. In 2007, Maglaras founded Mismi Inc., a financial technology firm based in New York City.
|
|
Marjorie "Molly" Greene Hahn (born December 30, 1948) is an American mathematician and tennis player. In mathematics and mathematical statistics she is known for her research in probability theory, including work on central limit theorems, stochastic processes, and stochastic differential equations. She is a professor emeritus of mathematics at Tufts University.
|
|
Stochastic dynamic programs can be solved to optimality by using backward recursion or forward recursion algorithms. Memoization is typically employed to enhance performance. However, like deterministic dynamic programming also its stochastic variant suffers from the curse of dimensionality. For this reason approximate solution methods are typically employed in practical applications.
|
|
Bensoussan, Alain. Stochastic control of partially observable systems. Cambridge University Press, 2004. He coauthored a number of influential books.
|
|
The stochastic version of kronecker graph eliminates the staircase effect, which happens due to large multiplicity of kronecker graph.
|
|
In economics, the Ramsey–Cass–Koopmans model is deterministic. The stochastic equivalent is known as Real Business Cycle theory.
|
|
His research interests include: model- based reinforcement learning, probabilistic inference in control system, learning dynamical system, stochastic optimal control.
|
|
Stochastic multicriteria acceptability analysis (SMAA) is a multiple-criteria decision analysis method for problems with missing or incomplete information.
|
|
This is the type of stochastic convergence that is most similar to pointwise convergence known from elementary real analysis.
|
|
Samuel Karlin and H. M. Taylor. "A First Course in Stochastic Processes." Academic Press, 1975 (second edition). Samuel Karlin.
|
|
Two-dimensional copulas are known in some other areas of mathematics under the name permutons and doubly-stochastic measures.
|
|
Sheynin, Oscar. "Stochastic Thinking in the Bible and the Talmud." Annals of Science 55, no. 2 (1998): 185-198.
|
|
A stochastic model of rainfall interception. Journal of Hydrology 89, 65–71. and Calder [1990].Calder, I. R., 1990.
|
|
More recently, stochastic circuits have been successfully used in image processing tasks such as edge detection and image thresholding.
|
|
In statistics, a doubly stochastic model is a type of model that can arise in many contexts, but in particular in modelling time-series and stochastic processes. The basic idea for a doubly stochastic model is that an observed random variable is modelled in two stages. In one stage, the distribution of the observed outcome is represented in a fairly standard way using one or more parameters. At a second stage, some of these parameters (often only one) are treated as being themselves random variables.
|
|
Professor Peng generalized the stochastic maximum principle in stochastic optimal control. In a paper published in 1990 with Étienne Pardoux, Peng founded the general theory (including nonlinear expectation) of backward stochastic differential equations (BSDEs), though linear BSDEs had been introduced by Jean-Michel Bismut in 1973. Soon Feynman–Kac type connections of BSDEs and certain kinds of elliptic and parabolic partial differential equations (PDEs), e.g., Hamilton–Jacobi–Bellman equation, were obtained, where the solutions of these PDEs can be interpreted in the classical or viscosity senses.
|
|
The development of an organism from single-celled to fully formed is a process with many, many steps. Even beginning with identical genomes, as in clones and identical twins, the process is unlikely to occur the same way twice. A process with this element of randomness is called a stochastic process, and cell differentiation is, in part, a stochastic process. The stochastic element of development is partly responsible for the eventual appearance of white on a horse, potentially accounting for nearly a quarter of the phenotype.
|
|
Stochastic semantic analysis is an approach used in computer science as a semantic component of natural language understanding. Stochastic models generally use the definition of segments of words as basic semantic units for the semantic models, and in some cases involve a two layered approach.Language Understanding Using Two-Level Stochastic Models by F. Pla, et al, 2001, Springer Lecture Notes in Computer Science Example applications have a wide range. In machine translation, it has been applied to the translation of spontaneous conversational speech among different languages.
|
|
In probability theory, a continuous stochastic process is a type of stochastic process that may be said to be "continuous" as a function of its "time" or index parameter. Continuity is a nice property for (the sample paths of) a process to have, since it implies that they are well-behaved in some sense, and, therefore, much easier to analyze. It is implicit here that the index of the stochastic process is a continuous variable. Some authorsDodge, Y. (2006) The Oxford Dictionary of Statistical Terms, OUP.
|
|
Around the beginning of the 21st century a number of new network technologies have arisen including mobile ad hoc networks and sensor networks. Stochastic geometry and percolation techniques have been used to develop models for these networks. The increases in user traffic has resulted in stochastic geometry being applied to cellular networks.
|
|
Stochastic texture synthesis methods produce an image by randomly choosing colour values for each pixel, only influenced by basic parameters like minimum brightness, average colour or maximum contrast. These algorithms perform well with stochastic textures only, otherwise they produce completely unsatisfactory results as they ignore any kind of structure within the sample image.
|
|
Other authors consider a point process as a stochastic process, where the process is indexed by sets of the underlying space on which it is defined, such as the real line or n-dimensional Euclidean space. Other stochastic processes such as renewal and counting processes are studied in the theory of point processes.
|
|
The mathematical space S of a stochastic process is called its state space. This mathematical space can be defined using integers, real lines, n-dimensional Euclidean spaces, complex planes, or more abstract mathematical spaces. The state space is defined using elements that reflect the different values that the stochastic process can take.
|
|
In mathematics, specifically in the theory of Markovian stochastic processes in probability theory, the Chapman–Kolmogorov equation is an identity relating the joint probability distributions of different sets of coordinates on a stochastic process. The equation was derived independently by both the British mathematician Sydney Chapman and the Russian mathematician Andrey Kolmogorov.
|
|
The result would be 0 with regular rounding, but with stochastic rounding, the expected result would be 30, which is the same value obtained without rounding. This can be useful in machine learning where the training may use low precision arithmetic iteratively. Stochastic rounding is a way to achieve 1-dimensional dithering.
|
|
In a direct dilution assay the amount of dose needed to produce a specific (fixed) response is measured, so that the dose is a stochastic variable defining the tolerance distribution. Conversely, in an indirect dilution assay the dose levels are administered at fixed dose levels, so that the response is a stochastic variable.
|
|
In mathematics -- specifically, in stochastic analysis -- Dynkin's formula is a theorem giving the expected value of any suitably smooth statistic of an Itō diffusion at a stopping time. It may be seen as a stochastic generalization of the (second) fundamental theorem of calculus. It is named after the Russian mathematician Eugene Dynkin.
|
|
Bismut's early work was related to stochastic differential equations, stochastic control, and Malliavin calculus, to which he made fundamental contributions. Bismut received in 1973 his Docteur d'État in Mathematics, from the Université Paris-VI, a thesis entitled Analyse convexe et probabilités. In his thesis, Bismut established a stochastic version of Pontryagin's maximum principle in control theory by introducing and studying the backward stochastic differential equations which have been the starting point of an intensive research in stochastic analysis and it stands now as a major tool in Mathematical Finance.[Preface by Paul Malliavin, From probability to geometry (I). Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque 327, (2009), xv--xvi] [The mathematical work of Jean-Michel Bismut: a brief summary, Astérisque 327, (2009), xxv--xxxvii] Using the quasi-invariance of the Brownian measure, Bismut gave a new approach to the Malliavin calculus and a probabilistic proof of Hörmander's theorem.
|
|
Navy Hydrographic Service, Paris, 153 p. and to stochastic simulation.André G. Journel (1974). Geostatistics for conditional simulation of ore bodies.
|
|
In a univariate context this is essentially the same as the well-known concept of compounded distributions. For the more general case of doubly stochastic models, there is the idea that many values in a time-series or stochastic model are simultaneously affected by the underlying parameters, either by using a single parameter affecting many outcome variates, or by treating the underlying parameter as a time- series or stochastic process in its own right. The basic idea here is essentially similar to that broadly used in latent variable models except that here the quantities playing the role of latent variables usually have an underlying dependence structure related to the time-series or spatial context. An example of a doubly stochastic model is the following.
|
|
Meyer is best known for his continuous-time analog of Doob's decomposition of a submartingale, known as the Doob–Meyer decomposition and his work on the 'general theory' of stochastic processes, published in his monumental book Probabilities and Potential, written with Claude Dellacherie. Some of his main areas of research in probability theory were the general theory of stochastic processes, Markov processes, stochastic integration, stochastic differential geometry and quantum probability. His most cited book is Probabilities and Potential B, written with Claude Dellacherie. The preceding book is the English translation of the second book in a series of five written by Meyer and Dellacherie from 1975 to 1992 and elaborated from Meyer's pioneering book Probabilités et Potentiel, published in 1966.
|
|
Mathematical models are based on mathematical equations and random events. The most common way to create compositions through mathematics is stochastic processes. In stochastic models a piece of music is composed as a result of non-deterministic methods. The compositional process is only partially controlled by the composer by weighting the possibilities of random events.
|
|
Dose-dependent blur aggravates photon shot noise, causing features to fail to print (red) or bridge the gap to the neighboring features (green). EUV lithography is particularly sensitive to stochastic effects.P. De Bisschop, “Stochastic effects in EUV lithography: random, local CD variability, and printing failures”, J. Micro/Nanolith. MEMS MOEMS 16(4), 041013 (2017).
|
|
Stochastic defects limit EUV resolution. Stochastic defects are more serious for tighter pitches; at 36 nm pitch defect rate does not drop below ~1e-9. Contact patterns have severe defectivity at larger dimensions. The most obvious case requiring multiple patterning is when the feature pitch is below the resolution limit of the optical projection system.
|
|
EMP SP is the stochastic extension of the EMP framework. A deterministic model with fixed parameters is transformed into a stochastic model where some of the parameters are not fixed but are represented by probability distributions. This is done with annotations and specific keywords. Single and joint discrete and parametric probability distributions are possible.
|
|
Polynomial chaos (PC), also called Wiener chaos expansion, is a non-sampling- based method to determine the evolution of uncertainty in a dynamical system when there is probabilistic uncertainty in the system parameters. PC was first introduced by Norbert Wiener using Hermite polynomials to model stochastic processes with Gaussian random variables. It can be thought of as an extension of Volterra's theory of nonlinear functionals for stochastic systems. According to Cameron and Martin such an expansion converges in the L_2 sense for any arbitrary stochastic process with finite second moment.
|
|
It also encourages increased awareness of the rapidly growing field of optimisation through publications, conferences, joint research and student exchange.Centre for Optimisation and its Applications His books include Stochastic Global Optimization, published in 2008 by Springer,Stochastic Global Optimization - Springer which received positive comments from reviewers,Stochastic Global Optimization - Springer (Reviews) Theory of Global Random Search, and Analysis of time series structure: SSA and related techniques. Zhigljavsky received an MSc in 1976, a PhD in 1981, and a Habilitation in 1987 from the St. Petersburg State University, Russia.
|
|
His research interests are in stochastic systems and database management. With the late Moshe Zakai, he originated a line of study in stochastic calculus now known as the Wong-Zakai Theorem. Wong was a co-designer of INGRES, one of the first modern database systems and the author of a major text on stochastic processes. From 1990 to 1993, Wong served as Associate Director of the White House Office of Science and Technology Policy, and from 1998 to 2000 he headed the Engineering Directorate of the National Science Foundation.
|
|
In supersymmetric theory of stochastics, an approximation-free theory of stochastic differential equations, 1/f noise is one of the manifestations of the spontaneous breakdown of topological supersymmetry. This supersymmetry is an intrinsic property of all stochastic differential equations and its meaning is the preservation of the continuity of the phase space by continuous time dynamics. Spontaneous breakdown of this supersymmetry is the stochastic generalization of the concept of deterministic chaos, whereas the associated emergence of the long-term dynamical memory or order, i.e., 1/f and crackling noises, the Butterfly effect etc.
|
|
In mathematics, constructions of mathematical objects are needed, which is also the case for stochastic processes, to prove that they exist mathematically. There are two main approaches for constructing a stochastic process. One approach involves considering a measurable space of functions, defining a suitable measurable mapping from a probability space to this measurable space of functions, and then deriving the corresponding finite-dimensional distributions. Another approach involves defining a collection of random variables to have specific finite-dimensional distributions, and then using Kolmogorov's existence theorem to prove a corresponding stochastic process exists.
|
|
This state space can be, for example, the integers, the real line or n-dimensional Euclidean space. An increment is the amount that a stochastic process changes between two index values, often interpreted as two points in time. A stochastic process can have many outcomes, due to its randomness, and a single outcome of a stochastic process is called, among other names, a sample function or realization. A single computer-simulated sample function or realization, among other terms, of a three-dimensional Wiener or Brownian motion process for time 0 ≤ t ≤ 2.
|
|
Figure 1: sample SSDM signal with average. Stochastic Signal Density Modulation (SSDM)US Patent 8129924 Stochastic signal density modulation for optical transducer control (Mar 6, 2012)US Patent 8476846 Stochastic signal density modulation for optical transducer control (Jul 2, 2013) is a novel power modulation technique primarily used for LED power control. The information is encoded - or the power level is set - using pulses that have pseudo random widths. The pulses are produced in such a way that on average the produced signal will have a desired ratio between high and low states.
|
|
In supersymmetric theory of SDEs, stochastic dynamics is defined via stochastic evolution operator acting on the differential forms on the phase space of the model. In this exact formulation of stochastic dynamics, all SDEs possess topological supersymmetry which represents the preservation of the continuity of the phase space by continuous time flow. The spontaneous breakdown of this supersymmetry is the mathematical essence of the ubiquitous dynamical phenomenon known across disciplines as chaos, turbulence, self-organized criticality etc. and the Goldstone theorem explains the associated long-range dynamical behavior, i.e.
|
|
Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables. Stochastic control aims to design the time path of the controlled variables that performs the desired control task with minimum cost, somehow defined, despite the presence of this noise.Definition from Answers.
|
|
The stochastic noise model can be described as a kind of "dumb" noise model. That is to say that it does not have the adaptability to deal with "intelligent" threats. Even if the attacker is bounded it is still possible that they might be able to overcome the stochastic model with a bit of cleverness. The stochastic model has no real way to fight against this sort of attack and as such is unsuited to dealing with the kind of "intelligent" threats that would be preferable to have defenses against.
|
|
If this assumption does not hold, stochastic computing can fail dramatically. For instance, if we try to compute p^2 by multiplying a bit stream for p by itself, the process fails: since a_i \land a_i=a_i, the stochastic computation would yield p \times p = p , which is not generally true (unless p=0 or 1). In systems with feedback, the problem of decorrelation can manifest in more complicated ways. Systems of stochastic processors are prone to latching, where feedback between different components can achieve a deadlocked state.
|
|
He became interested in probability theory through the study of Norbert Wiener's work. He was appointed Assistant professor at the Kyushu University in 1941. When Kiyosi Itô published his papers on stochastic differential equations in 1942, Maruyama immediately recognized the importance of this work and soon published a series of papers on stochastic differential equations and Markov processes. Maruyama is known in particular for his 1955 study of the convergence properties of the finite-difference approximations for the numerical solution of stochastic differential equations, now known as the Euler–Maruyama method.
|
|
Techniques to investigate data theft include stochastic forensics, digital artifact analysis (especially of USB drive artifacts), and other computer forensics techniques.
|
|
Stochastic analysis of non-slotted aloha in wireless ad hoc networks. In INFOCOM, 2010 Proceedings IEEE, pages 1–9. IEEE, 2010.
|
|
Nowadays stochastic resonance is commonly invoked when noise and nonlinearity concur to determine an increase of order in the system response.
|
|
In probability and mathematical statistics, Ignatov's theorem is a basic result on the distribution of record values of a stochastic process.
|
|
The index set of this stochastic process is the non-negative numbers, while its state space is three-dimensional Euclidean space.
|
|
T-distributed Stochastic Neighbor Embedding (t-SNE) is a non-linear dimensionality reduction technique useful for visualization of high- dimensional datasets.
|
|
Stochastic equicontinuity is a version of equicontinuity used in the context of sequences of functions of random variables, and their convergence.
|
|
If m = 1 is a root of multiplicity r, then the stochastic process is integrated of order r, denoted I(r).
|
|
Recursive trees can be generated using a simple stochastic process. Such random recursive trees are used as simple models for epidemics.
|
|
From January 24–28, 2000, he worked for the Center for Mathematical Physics and Stochastic at the University of Aarhus, Denmark.
|
|
Stochastic roadmap simulation is used to explore the kinetics of molecular motion by simultaneously examining multiple pathways in the roadmap. Ensemble properties of molecular motion (e.g., probability of folding (PFold), escape time in ligand-protein binding) is computed efficiently and accurately with stochastic roadmap simulation. PFold values are computed using the first step analysis of Markov chain theory.
|
|
Stochastic forensics has been criticized as only providing evidence and indications of data theft, and not concrete proof. Indeed, it requires a practitioner to "think like Sherlock, not Aristotle." Certain authorized activities besides data theft may cause similar disturbances in statistical distributions. Furthermore, many operating systems do not track access timestamps by default, making stochastic forensics not directly applicable.
|
|
This article was retracted in July 2020 because the authors made a sign error in their implementation of the benchmarked optimization algorithm. It was shown by Dries Sels that "a simple stochastic local optimization method finds near-optimal solutions which outperform all players". In other words, the 200 000 players were all beaten by the stochastic optimization method.
|
|
Rollo Davidson (b. Bristol, 8 October 1944, d. Piz Bernina, 29 July 1970) was a probabilist, alpinist, and Fellow-elect of Churchill College, Cambridge, who died aged 25 on Piz Bernina. He is known for his work on semigroups, stochastic geometry, and stochastic analysis, and for the Rollo Davidson Prize, given in his name to young probabilists.
|
|
The concept of semimartingales, and the associated theory of stochastic calculus, extends to processes taking values in a differentiable manifold. A process X on the manifold M is a semimartingale if f(X) is a semimartingale for every smooth function f from M to R. Stochastic calculus for semimartingales on general manifolds requires the use of the Stratonovich integral.
|
|
7nm EUV stochastic failure probability. 7nm features are expected to approach ~20 nm width. The probability of EUV stochastic failure is measurably high for the commonly applied dose of 30 mJ/cm2. The 7 nm foundry node is expected to utilize any of or a combination of the following patterning technologies: pitch splitting, self-aligned patterning, and EUV lithography.
|
|
In probability theory, independent increments are a property of stochastic processes and random measures. Most of the time, a process or random measure has independent increments by definition, which underlines their importance. Some of the stochastic processes that by definition possess independent increments are the Wiener process, all Lévy processes, all additive process and the Poisson point process.
|
|
Next was Gérard Cornuéjols (1999-2003) and Nimrod Megiddo (2004-2009). Finally came Uri Rothblum (2009-2012), Jim Dai (2012-2018), and the current editor-in-chief Katya Scheinberg (2019–present). The journal's three initial sections were game theory, stochastic systems, and mathematical programming. Currently, the journal has four sections: continuous optimization, discrete optimization, stochastic models, and game theory.
|
|
SDS is both an efficient and robust global search and optimisation algorithm, which has been extensively mathematically described.Nasuto, S.J., Bishop, J.M. & Lauria, S., Time complexity analysis of the Stochastic Diffusion Search, Proc. Neural Computation '98, pp. 260-266, Vienna, Austria, (1998).Nasuto, S.J., & Bishop, J.M., (1999), Convergence of the Stochastic Diffusion Search, Parallel Algorithms, 14:2, pp: 89-107.
|
|
In mathematics -- specifically, in stochastic analysis -- an Itô diffusion is a solution to a specific type of stochastic differential equation. That equation is similar to the Langevin equation used in physics to describe the Brownian motion of a particle subjected to a potential in a viscous fluid. Itô diffusions are named after the Japanese mathematician Kiyosi Itô.
|
|
The remaining droplets freeze in a stochastic way, at rates 0.02/s if they have one impurity particle, 0.04/s if they have two, and so on. These data are just one example, but they illustrate common features of the nucleation of crystals in that there is clear evidence for heterogeneous nucleation, and that nucleation is clearly stochastic.
|
|
A Boltzmann machine is a type of stochastic neural network invented by Geoffrey Hinton and Terry Sejnowski in 1985. Boltzmann machines can be seen as the stochastic, generative counterpart of Hopfield nets. They are named after the Boltzmann distribution in statistical mechanics. The units in Boltzmann machines are divided into two groups: visible units and hidden units.
|
|
By analyzing these properties statistically, stochastic mechanics can reconstruct activity that took place, even if the activity did not create any artifacts.
|
|
Stochastic Geometry and Wireless Networks, Volume II – Applications, volume 4, No 1-2 of Foundations and Trends in Networking. NoW Publishers, 2009.
|
|
D. Schuhmacher. Distance estimates for dependent superpositions of point processes. Stochastic processes and their applications, 115(11):1819–1837, 2005.D. Schuhmacher.
|
|
SAMPL shares all language features with AMPL, and adds some constructs specifically designed for expressing scenario based stochastic programming and robust optimization.
|
|
Stochastic modelling builds volatility and variability (randomness) into the simulation and therefore provides a better representation of real life from more angles.
|
|
Shih, and Y.-S. Chen. Stochastic geometry based models for modeling cellular networks in urban areas. Wireless Networks, pages 1–10, 2012.
|
|
Kalyanapuram Rangachari Parthasarathy (born 25 June 1936) is professor emeritus at the Indian Statistical Institute and a pioneer of quantum stochastic calculus.
|
|
Stochastic Geometry and Wireless Networks, Volume II – Applications, volume 4, No 1-2 of Foundations and Trends in Networking. NoW Publishers, 2009.
|
|
Other stochastic processes can satisfy the Markov property, the property that past behavior does not affect the process, only the present state.
|
|
Ruslan Leont'evich Stratonovich () was a Russian physicist, engineer, and probabilist and one of the founders of the theory of stochastic differential equations.
|
|
Stochastic Petri nets are a form of Petri net where the transitions fire after a probabilistic delay determined by a random variable.
|
|
Stochastic Network Optimization with Application to Communication and Queueing Systems, Morgan & Claypool, 2010. (see also Backpressure with utility optimization and penalty minimization).
|
|
The stochastic vacuum model is based on the approximation of nonperturbative QCD as a Gaussian process. It allows to calculate Wilson loops.
|
|
Van der Meer invented the technique of stochastic cooling of particle beams.Nobel Press Release. Nobelprize.org (17 October 1984). Retrieved on 3 April 2014.
|
|
In homogenization theory, a branch of mathematics, stochastic homogenization is a technique for understanding solutions to partial differential equations with oscillatory random coefficients.
|
|
7, pp. 2915–2934, July 2006. M. J. Neely, E. Modiano, and C. Li, "Fairness and Optimal Stochastic Control for Heterogeneous Networks," Proc.
|
|
L. Huang and M. J. Neely, "Delay Reduction via Lagrange Multipliers in Stochastic Network Optimization," IEEE Trans. on Automatic Control, vol. 56, no.
|
|
Peng Shige (, born December 8, 1947 in Binzhou, Shandong) is a Chinese mathematician noted for his contributions in stochastic analysis and mathematical finance.
|
|
Darinka Dentcheva (Bulgarian: Даринка Денчева) is a Bulgarian-American mathematician, noted for her contributions to convex analysis, stochastic programming, and risk-averse optimization.
|
|
SC Magazine He has also contributed to computer security, digital forensics, and software development.Grier, Jonathan (May 2012). "Investigating Data Theft with Stochastic Forensics".
|
|
Proving Large Deviation Principle for stochastic Navier-Stokes equation as a joint work with P. Sundar to estimate the probability of rare events.
|
|
Spatial stochastic process can become computationally effective and scalable Gaussian process models, such as Gaussian Predictive Processes and Nearest Neighbor Gaussian Processes (NNGP).
|
|
The combination of SSA and Copula-based methods have been applied for the first time as a novel stochastic tool for EOP prediction.
|
|
Using a special module, Calamus supports dot rasterization (using the term Star Screening) which is a frequency modulated method of halftoning (Stochastic screening).
|
|
Positive Results: # Every model that satisfies Linear Stochastic Transitivity must also satisfy Strong Stochastic Transitivity, which in turn must satisfy Weak Stochastic Transitivity. This is represented as: LST \implies SST\impliesWST ; # Since the Bradeley-Terry models and the are LST models, they also satisfy SST and WST; # Due to the convenience of , a few authors have identified axiomatic of linear stochastic transitivity (and other models), most notably Gérard Debreu showed that : + \implies LST (see also Debreu Theorems); # Two LST models given by invertible comparison functions F(x) and G(x) are if and only if F(x) = G(\kappa x)for some \kappa \geq 0. Negative Results: # Stochastic transitivity models are empirically , however, they may be falsifiable; # between LST comparison functions F(x) and G(x) can be impossible even if an infinite amount of data is provided over a finite number of ; # The for WST, SST and LST models are in general NP-Hard, however, near optimal polynomially computable estimation procedures are known for SST and LST models.
|
|
Kinematic dynamo can be also viewed as the phenomenon of the spontaneous breakdown of the topological supersymmetry of the associated stochastic differential equation related to the flow of the background matter. Within supersymmetric theory of stochastics, this supersymmetry is an intrinsic property of all stochastic differential equations, its meaning is the preservation of the continuity of the phase space of the model by continuous time flows, and its spontaneous breakdown is the stochastic generalization of the concept of deterministic chaos. In other words, kinematic dynamo is a manifestation of the chaoticity of the underlying flow of the background matter.
|
|
Another instance of the separation principle arises in the setting of linear stochastic systems, namely that state estimation (possibly nonlinear) together with an optimal state feedback controller designed to minimize a quadratic cost, is optimal for the stochastic control problem with output measurements. When process and observation noise are Gaussian, the optimal solution separates into a Kalman filter and a linear-quadratic regulator. This is known as linear-quadratic- Gaussian control. More generally, under suitable conditions and when the noise is a martingale (with possible jumps), again a separation principle applies and is known as the separation principle in stochastic control. . . . .
|
|
European Institute for Statistics, Probability, Stochastic Operations Research and its Applications (EURANDOM) is a research institute at the Eindhoven University of Technology, dedicated to fostering research in the stochastic sciences and their applications. The institute was founded in 1997 at the Eindhoven University of Technology to focus on project oriented research of "stochastic problems connected to industrial and societal applications."Committee on U.S. Mathematical Sciences Research Institutes (1999) U.S. Research Institutes in the Mathematical Sciences. p. 6 The institute actively attracts young talent for its research and doctoral programs, facilitates research and actively seeks European cooperation.
|
|
An example of a differential testing system that performs domain-specific coverage-guided input generation is Mucerts. Mucerts relies on the knowledge of the partial grammar of the X.509 certificate format and uses a stochastic sampling algorithm to drive its input generation while tracking the program coverage. Another line of research builds on the observation that the problem of new input generation from existing inputs can be modeled as a stochastic process. An example of a differential testing tool that uses such a stochastic process modeling for input generation is Chen et al.’s tool.
|
|
In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others. Stochastic volatility models are one approach to resolve a shortcoming of the Black–Scholes model.
|
|
At ultralight densities a further reduced cubic scaling law E∝ρ3 is common, such as with aerogels and aerogel composites. The dependence of scaling on geometry is seen in periodic lattice-based materials that have nearly ideal E∝ρ scaling, with high node connectedness relative to stochastic foams. These structures have previously been implemented only in relatively dense engineered materials. For the ultralight regime the E∝ρ2 scaling seen in denser stochastic cellular materials applies to electroplated tubular nickel micro-lattices, as well as carbon-based open-cell stochastic foams, including carbon microtube aerographite and graphene cork.
|
|
A significant Kruskal–Wallis test indicates that at least one sample stochastically dominates one other sample. The test does not identify where this stochastic dominance occurs or for how many pairs of groups stochastic dominance obtains. For analyzing the specific sample pairs for stochastic dominance, Dunn's test, pairwise Mann–Whitney tests with Bonferroni correction, or the more powerful but less well known Conover–Iman test are sometimes used. Since it is a non-parametric method, the Kruskal–Wallis test does not assume a normal distribution of the residuals, unlike the analogous one-way analysis of variance.
|
|
Between 1938 and 1945, Itô worked for the Japanese National Statistical Bureau, where he published two of his seminal works on probability and stochastic processes. After that he continued to develop his ideas on stochastic analysis with many important papers on the topic. In 1952, he became a Professor at the University of Kyoto where he remained until his retirement in 1979.
|
|
Higher orders of stochastic dominance have also been analyzed, as have generalizations of the dual relationship between stochastic dominance orderings and classes of preference functions. Arguably the most powerful dominance criterion relies on the accepted economic assumption of decreasing absolute risk aversion. This involves several analytical challenges and a research effort is on its way to address those. See, e.g.
|
|
Truncating and censoring of data can also be estimated using stochastic models. For instance, applying a non-proportional reinsurance layer to the best estimate losses will not necessarily give us the best estimate of the losses after the reinsurance layer. In a simulated stochastic model, the simulated losses can be made to "pass through" the layer and the resulting losses assessed appropriately.
|
|
Assign a zero when there is no influence. Thus obtain the weighted column stochastic supermatrix. #Compute the limit priorities of the stochastic supermatrix according to whether it is irreducible (primitive or imprimitive [cyclic]) or it is reducible with one being a simple or a multiple root and whether the system is cyclic or not. Two kinds of outcomes are possible.
|
|
In 2010, Grier introduced stochastic forensics as an alternative to traditional digital forensics which typically relies on digital artifacts. Stochastic forensics' chief application is investigation of data theft, especially by insiders. Grier was inspired by the statistical mechanics method used in physics. In 2001, Grier exposed several security flaws in a number of techniques then popular in Common Gateway Interface web applications.
|
|
Another phenomenon closely related to stochastic resonance is inverse stochastic resonance. It happens in the bistable dynamical systems having the limit cycle and stable fixed point solutions. In this case the noise of particular variance could efficiently inhibit spiking activity by moving the trajectory to the stable fixed point. It has been initially found in single neuron models, including classical Hodgkin-Huxley system.
|
|
In probability theory and related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. In particular, it allows the computation of derivatives of random variables. Malliavin calculus is also called the stochastic calculus of variations. P. Malliavin first initiated the calculus on infinite dimensional space.
|
|
Some areas may be overexposed, leading to excessive resist loss or crosslinking. The probability of stochastic failure increases exponentially as feature size decreases, and for the same feature size, increasing distance between features also significantly increases the probability. Line cuts which are relatively widely spaced are a significant issue. Yield requires detection of stochastic failures down to below 1e-12.
|
|
3R2 and 2R1, but not 3R1 and antitransitive.since, more generally, xRy and yRz implies x=y+1=z+2≠z+1, i.e. not xRz, for all x, y, z Unexpected examples of intransitivity arise in situations such as political questions or group preferences. Generalized to stochastic versions (stochastic transitivity), the study of transitivity finds applications of in decision theory, psychometrics and utility models.
|
|
Kakapo The influence of stochastic variation in demographic (reproductive and mortality) rates is much higher for small populations than large ones. Stochastic variation in demographic rates causes small populations to fluctuate randomly in size. This variation could be a result of unequal sex ratios, high variance in family size, inbreeding or fluctuating population size.Frankham, R., Briscoe, D. A., & Ballou, J. D. (2002).
|
|
The result is that FM screens exhibit a greater color gamut than conventional AM/XM halftone screen frequencies. The creation of a plate with stochastic screening is done the same way as is done with an AM/XM screen. A tone reproduction compensation curve is typically applied to align the stochastic screening to conventional AM/FM tone reproductions targets (e.g. ISO 12647-2).
|
|
Gisiro Maruyama was a Japanese mathematician, noted for his contributions to the study of stochastic processes. The Euler–Maruyama method for the numerical solution of stochastic differential equations bears his name. Maruyama was born in 1916 and graduated from Tohoku University, where he studied Fourier analysis and physics. He began his mathematical work with a paper on Fourier analysis in 1939.
|
|
Optimal paths in graphs with stochastic or multidimensional weights. Communications of the ACM, 26(9), pp.670-676. Despite considerable progress during the course of the past decade, it remains a controversial question how an optimal path should be defined and identified in stochastic road networks. In other words, there is no unique definition of an optimal path under uncertainty.
|
|
You may find such normal form transformations for relatively simple systems of ordinary differential equations, both deterministic and stochastic, via an interactive web site.
|
|
The notion of a kernel plays a crucial role in Bayesian probability as the covariance function of a stochastic process called the Gaussian process.
|
|
Evelyn Buckwar is a German mathematician specializing in stochastic differential equations. She is Professor for Stochastics at the Johannes Kepler University Linz in Austria.
|
|
However, more recent studies discovered stable co-expression patterns between TRA genes which are localized in close proximity, suggesting "order in this stochastic process".
|
|
In theoretical physics, stochastic quantization is a method for modelling quantum mechanics, introduced by Edward Nelson in 1966,; ; and streamlined by Parisi and Wu.
|
|
Mathematics applied to biomedical engineering. Analysis of blood cells concentrations as long-memory stochastic process, and fractal characteristics. Heart rate variability studies. Wavelet analysis.
|
|
Experiments performed after this at a slightly higher level of analysis establish behavioral effects of stochastic resonance in other organisms; these are described below.
|
|
Imre Fényes (; 29 July 1917 - 13 November 1977) was a Hungarian physicist who was the first to propose a stochastic interpretation of quantum mechanics.
|
|
This is particularly prohibitive for EUV, where even when the primary feature is printed at 80 mJ/cm2, the SRAF suffers from stochastic printing.
|
|
Medhi published many articles in peer reviewed international and national journals. He also published two books on stochastic processes each with over 500 citations.
|
|
This kind of random measure is often used when describing jumps of stochastic processes, in particular in Lévy–Itō decomposition of the Lévy processes.
|
|
Another method is symbolic modeling, which represents many mental objects using variables and rules. Other types of modeling include dynamic systems and stochastic modeling.
|
|
Some important approaches in simulation optimization are discussed below. Spall, J.C. (2003). Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control. Hoboken: Wiley.
|
|
Springer Publishing Company, Incorporated, 2012. can be used, which is different from other approaches such as robust optimization, stochastic optimization and Markov decision processes.
|
|
S. P. Meyn and R.L. Tweedie, 2005. Markov Chains and Stochastic Stability. Second edition to appear, Cambridge University Press, 2009. S. P. Meyn, 2007.
|
|
Lévy processes and infinite divisibility, 1999. a term used in the study of Lévy processes,V. Mandrekar and B. Rüdiger. Stochastic Integration in Banach Spaces.
|
|
Another example is discrete state random dynamical system; some elementary contradistinctions between Markov chain and random dynamical system descriptions of a stochastic dynamics are discussed.
|
|
Hadamard derivative is a concept of directional derivative for maps between Banach spaces. It is particularly suited for applications in stochastic programming and asymptotic statistics.
|
|
In particular, this implies that the number of stochastic languages is uncountable. A p-adic language is regular if and only if \eta is rational.
|
|
High efficiency of the robust design optimization is provided by the capabilities of IOSO algorithms to solve stochastic optimization problems with large level of noise.
|
|
Based on normalized scale transform, a new method via averaged stochastic resonance is presented to enhance the result of rolling element bearing fault detection furtherly.
|
|
In a stochastic model, the notion of the usual exogeneity, sequential exogeneity, strong/strict exogeneity can be defined. Exogeneity is articulated in such a way that a variable or variables is exogenous for parameter \alpha. Even if a variable is exogenous for parameter \alpha, it might be endogenous for parameter \beta. When the explanatory variables are not stochastic, then they are strong exogenous for all the parameters.
|
|
On the sites of gene regulatory loci bound by transcription factors the random switching between methylated and unmethylated states of DNA was observed. This is also referred as stochastic switching and it is linked to selective buffering of gene regulatory circuit against mutations and genetic diseases. Only rare genetic variants show the stochastic type of gene regulation. The study made by Onuchic et al.
|
|
For medical purposes, X-ray filters are used to selectively attenuate, or block out, low-energy rays during x-ray imaging (radiography). Low energy x-rays (less than 30 keV) contribute little to the resultant image as they are heavily absorbed by the patient's soft tissues (particularly the skin). Additionally, this absorption adds to the risk of stochastic (e.g. cancer) or non stochastic radiation effects (e.g.
|
|
File carving involves searching for known file headers within the disk image and reconstructing deleted materials. ;Stochastic forensics :A method which uses stochastic properties of the computer system to investigate activities lacking digital artifacts. Its chief use is to investigate data theft. ;Steganography : One of the techniques used to hide data is via steganography, the process of hiding data inside of a picture or digital image.
|
|
Candidate of Physics and Mathematics of Moscow State University, specialist in theory of probability, mathematical statistics, theory of probabilistic processes, theory of optimization, stochastic differential equations, computer modelling of stochastic processes, computer simulation. Worked as researcher of computer geometry in Russian Space Research Institute, in Moscow Machine Tools and Instruments Institute, in University of Aizu in Japan. Faculty member of the Department of Mathematics and Mechanics MSU.
|
|
The process also has many applications and is the main stochastic process used in stochastic calculus. It plays a central role in quantitative finance, where it is used, for example, in the Black–Scholes–Merton model. The process is also used in different fields, including the majority of natural sciences as well as some branches of social sciences, as a mathematical model for various random phenomena.
|
|
Random walks.. appear in the description of a wide variety of processes in biology,Goel N. W. and Richter-Dyn N., Stochastic Models in Biology (Academic Press, New York) 1974; . chemistryVan Kampen N. G., Stochastic Processes in Physics and Chemistry, revised and enlarged edition (North-Holland, Amsterdam) 1992; . and physics.Doi M. and Edwards S. F., The Theory of Polymer Dynamics (Clarendon Press, Oxford) 1986; .
|
|
This experiment discovered the W and Z bosons, fundamental particles that carry the weak nuclear force. Fermi National Accelerator Laboratory continues to use stochastic cooling in its antiproton source. The accumulated antiprotons are used in the Tevatron to collide with protons to create collisions at CDF and the D0 experiment. Stochastic cooling in the Tevatron at Fermilab was attempted, but was not fully successful.
|
|
Numerical solution of stochastic differential equations and especially stochastic partial differential equations is a young field relatively speaking. Almost all algorithms that are used for the solution of ordinary differential equations will work very poorly for SDEs, having very poor numerical convergence. A textbook describing many different algorithms is Kloeden & Platen (1995). Methods include the Euler–Maruyama method, Milstein method and Runge–Kutta method (SDE).
|
|
To develop suitable models with point processes in stochastic geometry, spatial statistics and related fields, there are number of useful transformations that can be performed on point processes including: thinning, superposition, mapping (or transformation of space), clustering, and random displacement.F. Baccelli and B. Błaszczyszyn. Stochastic Geometry and Wireless Networks, Volume I – Theory, volume 3, No 3–4 of Foundations and Trends in Networking. NoW Publishers, 2009.
|
|
There is a difference between forward and futures prices when interest rates are stochastic. This difference disappears when interest rates are deterministic. In the language of stochastic processes, the forward price is a martingale under the forward measure, whereas the futures price is a martingale under the risk-neutral measure. The forward measure and the risk neutral measure are the same when interest rates are deterministic.
|
|
Circuits work properly even when the inputs are misaligned temporally. As a result, stochastic systems can be designed to work with inexpensive locally generated clocks instead of using a global clock and an expensive clock distribution network. Finally, stochastic computing provides an estimate of the solution that grows more accurate as we extend the bit stream. In particular, it provides a rough estimate very rapidly.
|
|
Depending on the setting, the process has several equivalent definitions as well as definitions of varying generality owing to its many applications and characterizations. The Poisson point process can be defined, studied and used in one dimension, for example, on the real line, where it can be interpreted as a counting process or part of a queueing model; in higher dimensions such as the plane where it plays a role in stochastic geometry and spatial statistics;A. Baddeley. A crash course in stochastic geometry. Stochastic Geometry: Likelihood and Computation Eds OE Barndorff-Nielsen, WS Kendall, HNN van Lieshout (London: Chapman and Hall), pages 1–35, 1999.
|
|
A random field is a collection of random variables indexed by a n-dimensional Euclidean space or some manifold. In general, a random field can be considered an example of a stochastic or random process, where the index set is not necessarily a subset of the real line. But there is a convention that an indexed collection of random variables is called a random field when the index has two or more dimensions. If the specific definition of a stochastic process requires the index set to be a subset of the real line, then the random field can be considered as a generalization of stochastic process.
|
|
Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins. The study of the former is historically older in, for example, the law of evidence, while the mathematical treatment of dice began with the work of Cardano, Pascal and Fermat between the 16th and 17th century. Probability is distinguished from statistics; see history of statistics. While statistics deals with data and inferences from it, (stochastic) probability deals with the stochastic (random) processes which lie behind data or outcomes.
|
|
They have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time.
|
|
A stochastic process can be classified in different ways, for example, by its state space, its index set, or the dependence among the random variables. One common way of classification is by the cardinality of the index set and the state space. When interpreted as time, if the index set of a stochastic process has a finite or countable number of elements, such as a finite set of numbers, the set of integers, or the natural numbers, then the stochastic process is said to be in discrete time. If the index set is some interval of the real line, then time is said to be continuous.
|
|
The Wiener process is a stochastic process with stationary and independent increments that are normally distributed based on the size of the increments. The Wiener process is named after Norbert Wiener, who proved its mathematical existence, but the process is also called the Brownian motion process or just Brownian motion due to its historical connection as a model for Brownian movement in liquids. Realizations of Wiener processes (or Brownian motion processes) with drift () and without drift (). Playing a central role in the theory of probability, the Wiener process is often considered the most important and studied stochastic process, with connections to other stochastic processes.
|
|
It is important to disambiguate algorithmic randomness with stochastic randomness. Unlike algorithmic randomness, which is defined for computable (and thus deterministic) processes, stochastic randomness is usually said to be a property of a sequence that is a priori known to be generated (or is the outcome of) by an independent identically distributed equiprobable stochastic process. Because infinite sequences of binary digits can be identified with real numbers in the unit interval, random binary sequences are often called (algorithmically) random real numbers. Additionally, infinite binary sequences correspond to characteristic functions of sets of natural numbers; therefore those sequences might be seen as sets of natural numbers.
|
|
Recently, a very simple algorithm was introduced that is based on "stochastic acceptance".A. Lipowski, Roulette-wheel selection via stochastic acceptance (arXiv:1109.3627) The algorithm randomly selects an individual (say i) and accepts the selection with probability f_i/f_M, where f_M is the maximum fitness in the population. Certain analysis indicates that the stochastic acceptance version has a considerably better performance than versions based on linear or binary search, especially in applications where fitness values might change during the run.Fast Proportional Selection While the behavior of this algorithm is typically fast, some fitness distributions (such as exponential distributions) may require O(n) iterations in the worst case.
|
|
A major drawback to Dropout is that it does not have the same benefits for convolutional layers, where the neurons are not fully connected. In stochastic pooling, the conventional deterministic pooling operations are replaced with a stochastic procedure, where the activation within each pooling region is picked randomly according to a multinomial distribution, given by the activities within the pooling region. This approach is free of hyperparameters and can be combined with other regularization approaches, such as dropout and data augmentation. An alternate view of stochastic pooling is that it is equivalent to standard max pooling but with many copies of an input image, each having small local deformations.
|
|
In the supersymmetric theory of SDEs, stochastic evolution is defined via stochastic evolution operator (SEO) acting on differential forms of the phase space. The Itô-Stratonovich dilemma takes the form of the ambiguity of the operator ordering that arises on the way from the path integral to the operator representation of stochastic evolution. The Itô interpretation corresponds to the operator ordering convention that all the momentum operators act after all the position operators. The SEO can be made unique by supplying it with its most natural mathematical definition of the pullback induced by the noise-configuration-dependent SDE-defined diffeomorphisms and averaged over the noise configurations.
|
|
Springer, 2015. but some choose to use the two terms for Poisson points processes defined on two different underlying spaces.D. Applebaum. Lévy processes and stochastic calculus.
|
|
T. V. Nguyen and F. Baccelli. A stochastic geometry model for cognitive radio networks. Comput. J., 55(5):534–552, 2012. and Strauss and Ginibre processes.
|
|
He thesis was published in 1978 with the title, "Mathematical Modelling of the Dynamics of Interacting Microbial Populations. Extinction Probabilities in a Stochastic Competition and Predation".
|
|
In addition to the key-route search approach, variations of the method include the approach that is aggregative and stochastic, considers decay in knowledge diffusion, etc.
|
|
Neural cryptography is a branch of cryptography dedicated to analyzing the application of stochastic algorithms, especially artificial neural network algorithms, for use in encryption and cryptanalysis.
|
|
Additionally, obtaining samples from a posterior distribution permits uncertainty quantification by means of confidence intervals, a feature which is not possible using traditional stochastic gradient descent.
|
|
The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating a stochastic process. The Snell envelope is named after James Laurie Snell.
|
|
The stochastic effects of radiation exposure in the Chernobyl liquidator population. Radiation Research Society 44th Annual Meeting, Chicago, Illinois, April 17, 1996.Beebe, G. W. (1998).
|
|
Rolf Schneider is known for his solution of Shephard's problem, his books on stochastic and integral geometry, and his comprehensive monography on the Brunn–Minkowski theory.
|
|
The objective of the stochastic scheduling problems can be regular objectives such as minimizing the total flowtime, the makespan, or the total tardiness cost of missing the due dates; or can be irregular objectives such as minimizing both earliness and tardiness costs of completing the jobs, or the total cost of scheduling tasks under likely arrival of a disastrous event such as a severe typhoon. The performance of such systems, as evaluated by a regular performance measure or an irregular performance measure, can be significantly affected by the scheduling policy adopted to prioritize over time the access of jobs to resources. The goal of stochastic scheduling is to identify scheduling policies that can optimize the objective. Stochastic scheduling problems can be classified into three broad types: problems concerning the scheduling of a batch of stochastic jobs, multi-armed bandit problems, and problems concerning the scheduling of queueing systems .
|
|
Particularly, we can view rumor spread as a stochastic process in social networks. While the microscopic models are more interested more on the micro intereactions between individuals.
|
|
Published 2004Y. Cao, H. Li, and L. Petzold. Efficient formulation of the stochastic simulation algorithm for chemically reacting systems, J. Chem. Phys, 121(9):4059–4067, 2004.
|
|
Later inverse stochastic resonance has been confirmed in Purkinje cells of cerebellum, where it could play the role for generation of pauses of spiking activity in vivo.
|
|
A stochastic neural network introduces random variations into the network. Such random variations can be viewed as a form of statistical sampling, such as Monte Carlo sampling.
|
|
Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
|
|
Results of Ray–Knight type for more general stochastic processes have been intensively studied, and analogue statements of both () and () are known for strongly symmetric Markov processes.
|
|
Description and preview. • 1971. "Stochastic Stability of a General Equilibrium System under Adaptive Expectations" (with Stephen J. Turnovsky), International Economic Review, 12(1), pp. 71–86. • 1974.
|
|
Together with Xue-Mei Li and Yves Le Jan he wrote the books "The Geometry of Filtering" and "On the Geometry of Diffusion Operators and Stochastic Flows".
|
|
Alexei Zamolodchikov. Mccme.ru. Retrieved on 21 May 2016. He died in Moscow. The Liouville field theory and stochastic models seminar was held in his honor in 2008.
|
|
Lecture Notes in Computer Science 4702 (2007) 164-175. Having stated the probabilistic model for ordinal classification problems with monotonicity constraints, the concepts of lower approximations are extended to the stochastic case. The method is based on estimating the conditional probabilities using the nonparametric maximum likelihood method which leads to the problem of isotonic regression. Stochastic dominance-based rough sets can also be regarded as a sort of variable-consistency model.
|
|
Stochastic games were introduced by Lloyd Shapley in 1953. The first paper studied the discounted two-person zero-sum stochastic game with finitely many states and actions and demonstrates the existence of a value and stationary optimal strategies. The study of the undiscounted case evolved in the following three decades, with solutions of special cases by Blackwell and Ferguson in 1968Blackwell and Ferguson,1968. "The Big Match", Ann. Math. Statist.
|
|
The Wilkie investment model, often just called Wilkie model, is a stochastic asset model developed by A. D. Wilkie that describes the behavior of various economics factors as stochastic time series. These time series are generated by autoregressive models. The main factor of the model which influences all asset prices is the consumer price index. The model is mainly in use for actuarial work and asset liability management.
|
|
If a family of distributions f_\theta(x) has the monotone likelihood ratio property in T(X), # the family has monotone decreasing hazard rates in \theta (but not necessarily in T(X)) # the family exhibits the first-order (and hence second-order) stochastic dominance in x, and the best Bayesian update of \theta is increasing in T(X). But not conversely: neither monotone hazard rates nor stochastic dominance imply the MLRP.
|
|
Hybrid stochastic simulation is sub-class of stochastic simulations, designed to simulate part of Brownian trajectories avoiding to simulate the entire trajectories. This approach is particularly relevant when a Brownian particle evolves in an infinite space. Trajectories are then simulated only in the neighborwod of small targets. Otherwise, explicit analytical expression are used to map the initial point to a distribution located on a imaginary surface around the targets.
|
|
Stochastic dominance is a partial order between random variables. It is a form of stochastic ordering. The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble for a broad class of decision-makers. It is based on shared preferences regarding sets of possible outcomes and their associated probabilities.
|
|
Many aspects of such an evolutionary process are stochastic. Changed pieces of information due to recombination and mutation are randomly chosen. On the other hand, selection operators can be either deterministic, or stochastic. In the latter case, individuals with a higher fitness have a higher chance to be selected than individuals with a lower fitness, but typically even the weak individuals have a chance to become a parent or to survive.
|
|
Events are often triggered when a stochastic or random process first encounters a threshold. The threshold can be a barrier, boundary or specified state of a system. The amount of time required for a stochastic process, starting from some initial state, to encounter a threshold for the first time is referred to variously as a first hitting time. In statistics, first- hitting-time models are a sub-class of survival models.
|
|
The Birkhoff polytope Bn (also called the assignment polytope, the polytope of doubly stochastic matrices, or the perfect matching polytope of the complete bipartite graph K_{n,n}) is the convex polytope in RN (where N = n2) whose points are the doubly stochastic matrices, i.e., the matrices whose entries are non-negative real numbers and whose rows and columns each add up to 1. It is named after Garrett Birkhoff.
|
|
In mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the parameters of the model. The SABR model is widely used by practitioners in the financial industry, especially in the interest rate derivative markets. It was developed by Patrick S. Hagan, Deep Kumar, Andrew Lesniewski, and Diana Woodward.
|
|
Nelson made contributions to the theory of infinite-dimensional group representations, the mathematical treatment of quantum field theory, the use of stochastic processes in quantum mechanics, and the reformulation of probability theory in terms of non-standard analysis. For many years he worked on mathematical physics and probability theory, and he retained a residual interest in these fields, particularly in connection with possible extensions of stochastic mechanics to field theory.
|
|
Stochastic dynamic programming is a useful tool in understanding decision making under uncertainty. The accumulation of capital stock under uncertainty is one example; often it is used by resource economists to analyze bioeconomic problemsHowitt, R., Msangi, S., Reynaud, A and K. Knapp. 2002. "Using Polynomial Approximations to Solve Stochastic Dynamic Programming Problems: or A "Betty Crocker " Approach to SDP." University of California, Davis, Department of Agricultural and Resource Economics Working Paper.
|
|
This brief description has focused on the theory of stochastic geometry, which allows a view of the structure of the subject. However, much of the life and interest of the subject, and indeed many of its original ideas, flow from a very wide range of applications, for example: astronomy, spatially distributed telecommunications, wireless network modeling and analysis,M. Haenggi. Stochastic geometry for wireless networks. Cambridge University Press, 2012.
|
|
European Journal of Operational Research, 2(6):429–444. and Stochastic Frontier Analysis Aigner, D. J., Lovell, C. A. K. & Schmidt, P. (1977), ‘Formulation and estimation of stochastic frontier production functions’, Journal of Econometrics 6(1), 21–37. , among other methods. (E.g., see the recent book by Sickles and Zelenyuk (2019) for comprehensive coverage of the theory and related estimation and many references therein.) Sickles, R., & Zelenyuk, V. (2019).
|
|
These models quantify the uncertainty in the "true" value of the parameter of interest by probability distribution functions. They have been traditionally classified as stochastic programming and stochastic optimization models. Recently, probabilistically robust optimization has gained popularity by the introduction of rigorous theories such as scenario optimization able to quantify the robustness level of solutions obtained by randomization. These methods are also relevant to data-driven optimization methods.
|
|
James Ritchie Norris (born 29 August 1960) is a mathematician working in probability theory and stochastic analysis. He is the Professor of Stochastic Analysis in the Statistical Laboratory, University of Cambridge. He has made contributions to areas of mathematics connected to probability theory and mathematical analysis, including Malliavin calculus, heat kernel estimates, and mathematical models for coagulation and fragmentation. He was awarded the Rollo Davidson Prize in 1997.
|
|
In mathematics -- specifically, in stochastic analysis -- the Green measure is a measure associated to an Itō diffusion. There is an associated Green formula representing suitably smooth functions in terms of the Green measure and first exit times of the diffusion. The concepts are named after the British mathematician George Green and are generalizations of the classical Green's function and Green formula to the stochastic case using Dynkin's formula.
|
|
With Vincent Bansaye, Méléard is the author of Stochastic Models for Structured Populations: Scaling Limits and Long Time Behavior (Springer, 2015). She is also the author of Modèles aléatoires en ecologie et evolution [Random models in ecology and evolution] (Springer, 2016). As of 2018, she is the editor-in- chief of the journal Stochastic Processes and Their Applications and, as editor, an executive member in the Bernoulli Society.
|
|
The remarkable property of Solomonoff's induction is its completeness. In essence, the completeness theorem guarantees that the expected cumulative errors made by the predictions based on Solomonoff's induction are upper-bounded by the Kolmogorov complexity of the (stochastic) data generating process. The errors can be measured using the Kullback–Leibler divergence or the square of the difference between the induction's prediction and the probability assigned by the (stochastic) data generating process.
|
|
In consequence, only probabilistic models applied to molecular populations can be employed to describe it. Two such models of the statistical mechanics, due to Einstein and Smoluchowski are presented below. Another, pure probabilistic class of models is the class of the stochastic process models. There exist sequences of both simpler and more complicated stochastic processes which converge (in the limit) to Brownian motion (see random walk and Donsker's theorem).
|
|
However, during development its editors became concerned about the many different opinions on the risk of stochastic effects. The Commission therefore asked a working group to consider these, and their report, Publication 8 (1966), for the first time for the ICRP summarised the current knowledge about radiation risks, both somatic and genetic. Publication 9 then followed, and substantially changed radiation protection emphasis by moving from deterministic to stochastic effects.
|
|
A great deal of effort must be spent decorrelating the system to attempt to remediate latching. Fourth, although some digital functions have very simple stochastic counterparts (such as the translation between multiplication and the AND gate), many do not. Trying to express these functions stochastically may cause various pathologies. For instance, stochastic decoding requires the computation of the function f(p,q)\rightarrow pq/(pq + (1-p)(1-q)).
|
|
Pasik- Duncan's research concerns stochastic control and its applications in communications, economics, and health science. She is also interested in mathematics education, particularly for women in STEM fields..
|
|
In applied probability, a dynamic contagion process is a point process with stochastic intensity that generalises the Hawkes process and Cox process with exponentially decaying shot noise intensity.
|
|
Stochastic computing was first introduced in a pioneering paper by von Neumann in 1953. However, the theory could not be implemented until advances in computing of the 1960s.
|
|
On one hand, the demand can be stochastic (uncertain) or deterministic. On the other hand, it can be considered static (constant over time) or dynamic (e.g., having seasonality).
|
|
Neuronal activity at the microscopic level has a stochastic character, with atomic collisions and agitation, that may be termed "noise."Destexhe, A. (2012). Neuronal noise. New York: Springer.
|
|
Andrzej Piotr Ruszczyński (born July 29, 1951) is a Polish-American applied mathematician, noted for his contributions to mathematical optimization, in particular, stochastic programming and risk-averse optimization.
|
|
In mathematics, a reversible diffusion is a specific example of a reversible stochastic process. Reversible diffusions have an elegant characterization due to the Russian mathematician Andrey Nikolaevich Kolmogorov.
|
|
His research concerns probability, mathematical physics, quantum integrable systems, stochastic PDEs, and random matrix theory. He is particularly known for work related to the Kardar–Parisi–Zhang equation.
|
|
Peter Vaughan Elsmere McClintock (born 17 October 1940, Omagh, Northern Ireland) is notable for his scientific work on superfluids and stochastic nonlinear dynamics.IEEE Trans. Circ. & Sys.—II, Vol.
|
|
The first hitting time, also called first passage time, of the barrier set B with respect to an instance of a stochastic process is the time until the stochastic process first enters B. More colloquially, a first passage time in a stochastic system, is the time taken for a state variable to reach a certain value. Understanding this metric allows one to further understand the physical system under observation, and as such has been the topic of research in very diverse fields, from economics to ecology.Redner 2001 The idea that a first hitting time of a stochastic process might describe the time to occurrence of an event has a long history, starting with an interest in the first passage time of Wiener diffusion processes in economics and then in physics in the early 1900s.Bachelier 1900Von E 1900Smoluchowski 1915 Modeling the probability of financial ruin as a first passage time was an early application in the field of insurance.
|
|
In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. The transformation is also known as Hotelling transform and eigenvector transform, and is closely related to principal component analysis (PCA) technique widely used in image processing and in data analysis in many fields.Karhunen–Loeve transform (KLT), Computer Image Processing and Analysis (E161) lectures, Harvey Mudd College Stochastic processes given by infinite series of this form were first considered by Damodar Dharmananda Kosambi.. There exist many such expansions of a stochastic process: if the process is indexed over , any orthonormal basis of yields an expansion thereof in that form. The importance of the Karhunen–Loève theorem is that it yields the best such basis in the sense that it minimizes the total mean squared error.
|
|
In this case the stochastic term is stationary and hence there is no stochastic drift, though the time series itself may drift with no fixed long-run mean due to the deterministic component f(t) not having a fixed long-run mean. This non-stochastic drift can be removed from the data by regressing y_t on t using a functional form coinciding with that of f, and retaining the stationary residuals. In contrast, a unit root (difference stationary) process evolves according to :y_t = y_{t-1} + c + u_t where u_t is a zero-long-run-mean stationary random variable; here c is a non-stochastic drift parameter: even in the absence of the random shocks ut, the mean of y would change by c per period. In this case the non-stationarity can be removed from the data by first differencing, and the differenced variable z_t = y_t - y_{t-1} will have a long-run mean of c and hence no drift.
|
|
In applied mathematics, the "Gittins index" is a real scalar value associated to the state of a stochastic process with a reward function and with a probability of termination. It is a measure of the reward that can be achieved by the process evolving from that state on, under the probability that it will be terminated in future. The "index policy" induced by the Gittins index, consisting of choosing at any time the stochastic process with the currently highest Gittins index, is the solution of some stopping problems such as the one of dynamic allocation, where a decision-maker has to maximize the total reward by distributing a limited amount of effort to a number of competing projects, each returning a stochastic reward. If the projects are independent from each other and only one project at a time may evolve, the problem is called multi- armed bandit (one type of Stochastic scheduling problems) and the Gittins index policy is optimal.
|
|
Later in the 1960s and 1970s fundamental work was done by Alexander Wentzell in the Soviet Union and Monroe D. Donsker and Srinivasa Varadhan in the United States of America, which would later result in Varadhan winning the 2007 Abel Prize. In the 1990s and 2000s the theories of Schramm–Loewner evolution and rough paths were introduced and developed to study stochastic processes and other mathematical objects in probability theory, which respectively resulted in Fields Medals being awarded to Wendelin Werner in 2008 and to Martin Hairer in 2014. The theory of stochastic processes still continues to be a focus of research, with yearly international conferences on the topic of stochastic processes.
|
|
If the random variables are indexed by the Cartesian plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects. Based on their mathematical properties, stochastic processes can be grouped into various categories, which include random walks, martingales, Markov processes, Lévy processes, Gaussian processes, random fields, renewal processes, and branching processes. The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis.
|
|
Ionizing radiation has deterministic and stochastic effects on human health. Deterministic (acute tissue effect) events happen with certainty, with the resulting health conditions occurring in every individual who received the same high dose. Stochastic (cancer induction and genetic) events are inherently random, with most individuals in a group failing to ever exhibit any causal negative health effects after exposure, while an indeterministic random minority do, often with the resulting subtle negative health effects being observable only after large detailed epidemiology studies. The use of the sievert implies that only stochastic effects are being considered, and to avoid confusion deterministic effects are conventionally compared to values of absorbed dose expressed by the SI unit gray (Gy).
|
|
Recurrence period density entropy (RPDE) is a method, in the fields of dynamical systems, stochastic processes, and time series analysis, for determining the periodicity, or repetitiveness of a signal.
|
|
An example of a continuous-time stochastic process for which sample paths are not continuous is a Poisson process. An example with continuous paths is the Ornstein–Uhlenbeck process.
|
|
Let (X_t, Y_t) represent a pair of stochastic processes that are jointly wide-sense stationary. Then the Cross-covariance function and the cross-correlation function are given as follows.
|
|
He has served on numerous editorial boards, including those of Infinite Dimensional Analysis, Quantum Probability, and Related Topics IDAQP, Reviews in Mathematical Physics, and the Journal of Stochastic AnalysisJOSA.
|
|
Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. Stochastic partial differential equations generalize partial differential equations for modeling randomness.
|
|
Boxma's research focuses on the field of applied probability and stochastic operations, particularly of queueing theory and its application to the performance analysis of computer, communication and production systems.
|
|
Topics include Image classification, Stochastic gradient descent, Natural Language Processing and various deep learning architectures such as Convolutional Neural Networks, Recursive neural networks (RNNs) and Generative Adversarial Networks (GANs).
|
|
Department of Statistical Analysis of Natural Resource Data (SAND) works with project-oriented applied research statistics related to the petroleum industry. The group is a significant international contributor to research and services within reservoir description, stochastic modeling and geostatistics for the petroleum industry. The primary goal is to use statistical methods to reduce and quantify risk and uncertainty. The main area is stochastic modeling of the geology in petroleum reservoirs including upscaling and history matching.
|
|
His highest cited paper is The pricing of options on assets with stochastic volatilities at 4900 citations, according to Google Scholar. His research is in the areas of executive stock options, the rating of structured finance products and in best practice risk management approaches. With John Hull, he has made "seminal contributions" to the literature on stochastic volatility models, and credit derivative models. He is the co-author of Hull-White On Derivatives ().
|
|
In the theory of stochastic processes in discrete time, a part of the mathematical theory of probability, the Doob decomposition theorem gives a unique decomposition of every adapted and integrable stochastic process as the sum of a martingale and a predictable process (or "drift") starting at zero. The theorem was proved by and is named for Joseph L. Doob., see The analogous theorem in the continuous-time case is the Doob–Meyer decomposition theorem.
|
|
They argue that such situations should be rare for theoretical reasons, and that no real-world cases of private locked-in inefficiencies exist. Vergne and Durand qualify this critique by specifying the conditions under which path dependence theory can be tested empirically. Technically, a path-dependent stochastic process has an asymptotic distribution that "evolves as a consequence (function of) the process's own history". This is also known as a non-ergodic stochastic process.
|
|
Statistical mechanics, however, doesn't attempt to track properties of individual particles, but only the properties which emerge statistically. Hence, it can analyze complex systems without needing to know the exact position of their individual particles. Likewise, modern day computer systems, which can have over 2^{8^{10^{12}}} states, are too complex to be completely analyzed. Therefore, stochastic forensics views computers as a stochastic process, which, although unpredictable, has well defined probabilistic properties.
|
|
Kronecker graphs are a construction for generating graphs for modeling systems. The method constructs a sequence of graphs from a small base graph by iterating the Kronecker product.. A variety of generalizations of Kronecker graphs exist. The Graph500 benchmark for supercomputers is based on the use of a stochastic version of Kronecker graphs. Stochastic kronecker graph is a kronecker graph with each component of the matrix made by real numbers between 0 and 1.
|
|
Only limited knowledge of preferences is required for determining dominance. Risk aversion is a factor only in second order stochastic dominance. Stochastic dominance does not give a total order, but rather only a partial order: for some pairs of gambles, neither one stochastically dominates the other, since different members of the broad class of decision-makers will differ regarding which gamble is preferable without them generally being considered to be equally attractive.
|
|
The notion of ε-equilibria is important in the theory of stochastic games of potentially infinite duration. There are simple examples of stochastic games with no Nash equilibrium but with an ε-equilibrium for any ε strictly bigger than 0. Perhaps the simplest such example is the following variant of Matching Pennies, suggested by Everett. Player 1 hides a penny and Player 2 must guess if it is heads up or tails up.
|
|
A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. Distributions of potential outcomes are derived from a large number of simulations (stochastic projections) which reflect the random variation in the input(s). Its application initially started in physics.
|
|
His early work was directed toward generalizations of the central limit theorem, known as random evolution, on which he wrote a monograph in 1991. At the same time he became interested in differential equations with noise, computing the Lyapunov exponents of various stochastic differential equations. His many interests include classical harmonic analysis and stochastic Riemannian geometry. The Pinsky phenomenon, a term coined by J.P. Kahane, has become a popular topic for research in harmonic analysis.
|
|
In stochastic processes, the Stratonovich integral (developed simultaneously by Ruslan Stratonovich and Donald Fisk) is a stochastic integral, the most common alternative to the Itô integral. Although the Itô integral is the usual choice in applied mathematics, the Stratonovich integral is frequently used in physics. In some circumstances, integrals in the Stratonovich definition are easier to manipulate. Unlike the Itô calculus, Stratonovich integrals are defined such that the chain rule of ordinary calculus holds.
|
|
Stochastic Geometry and Wireless Networks, Volume I – Theory, volume 3, No 3-4 of Foundations and Trends in Networking. NoW Publishers, 2009. In other words, if the number of points of a point process located in some region of space is a random variable, then the first moment measure corresponds to the first moment of this random variable.D. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. Stochastic geometry and its applications, volume 2.
|
|
In a generalization called the "restless bandit problem", the states of non-played arms can also evolve over time. There has also been discussion of systems where the number of choices (about which arm to play) increases over time. Computer science researchers have studied multi-armed bandits under worst-case assumptions, obtaining algorithms to minimize regret in both finite and infinite (asymptotic) time horizons for both stochastic and non-stochastic arm payoffs.
|
|
The stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets characterized by being connected with one another with particular edge densities. For example, edges may be more common within communities than between communities. The stochastic block model is important in statistics, machine learning, and network science, where it serves as a useful benchmark for the task of recovering community structure in graph data.
|
|
Mechanistically, promoter escape occurs through DNA scrunching, providing the energy needed to break interactions between RNA polymerase holoenzyme and the promoter. In bacteria, it was historically thought that the sigma factor is definitely released after promoter clearance occurs. This theory had been known as the obligate release model. However, later data showed that upon and following promoter clearance, the sigma factor is released according to a stochastic model known as the stochastic release model.
|
|
If the HMMs are used for time series prediction, more sophisticated Bayesian inference methods, like Markov chain Monte Carlo (MCMC) sampling are proven to be favorable over finding a single maximum likelihood model both in terms of accuracy and stability.Sipos, I. Róbert. Parallel stratified MCMC sampling of AR-HMMs for stochastic time series prediction. In: Proceedings, 4th Stochastic Modeling Techniques and Data Analysis International Conference with Demographics Workshop (SMTDA2016), pp. 295-306.
|
|
There are also applications governed by deterministic principles whose description is so complex or unwieldy that it makes sense to consider probabilistic approximations. Every element of a graph dynamical system can be made stochastic in several ways. For example, in a sequential dynamical system the update sequence can be made stochastic. At each iteration step one may choose the update sequence w at random from a given distribution of update sequences with corresponding probabilities.
|
|
In addition to the properties of general risk measures, distortion risk measures also have: # Law invariant: If the distribution of X and Y are the same then \rho_g(X) = \rho_g(Y). # Monotone with respect to first order stochastic dominance. ## If g is a concave distortion function, then \rho_g is monotone with respect to second order stochastic dominance. # g is a concave distortion function if and only if \rho_g is a coherent risk measure.
|
|
Sankhya, the statistical journal published by ISI, was founded in 1933, along the lines of Karl Pearson's Biometrika. Mahalanobis was the founder editor. Each volume of Sankhya consists of four issues; two of them are in Series A, containing articles on theoretical statistics, probability theory and stochastic processes, and the other two issues form the Series B, containing articles on applied statistics, i.e. applied probability, applied stochastic processes, econometrics and statistical computing.
|
|
A stochastic process St is said to follow a GBM if it satisfies the following stochastic differential equation (SDE): : dS_t = \mu S_t\,dt + \sigma S_t\,dW_t where W_t is a Wiener process or Brownian motion, and \mu ('the percentage drift') and \sigma ('the percentage volatility') are constants. The former is used to model deterministic trends, while the latter term is often used to model a set of unpredictable events occurring during this motion.
|
|
An entirely classical derivation and interpretation of Schrödinger's wave equation by analogy with Brownian motion was suggested by Princeton University professor Edward Nelson in 1966. Similar considerations had previously been published, for example by R. Fürth (1933), I. Fényes (1952), and Walter Weizel (1953), and are referenced in Nelson's paper. More recent work on the stochastic interpretation has been done by M. Pavon. An alternative stochastic interpretation was developed by Roumen Tsekov.
|
|
In probability theory, stochastic drift is the change of the average value of a stochastic (random) process. A related concept is the drift rate, which is the rate at which the average changes. For example, a process that counts the number of heads in a series of n fair coin tosses has a drift rate of 1/2 per toss. This is in contrast to the random fluctuations about this average value.
|
|
First published in 1989 Stochastic diffusion search (SDS)Bishop, J.M., Stochastic Searching Networks, Proc. 1st IEE Int. Conf. on Artificial Neural Networks, pp. 329-331, London, UK, (1989).Nasuto, S.J. & Bishop, J.M., (2008), Stabilizing swarm intelligence search via positive feedback resource allocation, In: Krasnogor, N., Nicosia, G, Pavone, M., & Pelta, D. (eds), Nature Inspired Cooperative Strategies for Optimization, Studies in Computational Intelligence, vol 129, Springer, Berlin, Heidelberg, New York, pp. 115-123.
|
|
At this point, both the parent and offspring rules are returned to [P]. The LCS genetic algorithm is highly elitist since each learning iteration, the vast majority of the population is preserved. Rule discovery may alternatively be performed by some other method, such as an estimation of distribution algorithm, but a GA is by far the most common approach. Evolutionary algorithms like the GA employ a stochastic search, which makes LCS a stochastic algorithm.
|
|
In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani's 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion. However, it turns out that for a large class of semi- elliptic second-order partial differential equations the associated Dirichlet boundary value problem can be solved using an Itō process that solves an associated stochastic differential equation.
|
|
They are designed to provide a stochastic transfer function to approximate the quantity, duration, and quality of BMP effluent given the associated inflow values for a population of storm events.
|
|
Beginning in 2000, at Arizona State, she studied pink noise and stochastic resonance, which she applied to epidemic models in biostatistics as well as to the firing patterns of neurons.
|
|
NoW Publishers, 2009.F. Baccelli and B. Błaszczyszyn. Stochastic Geometry and Wireless Networks, Volume II – Applications, volume 4, No 1-2 of Foundations and Trends in Networking. NoW Publishers, 2009.
|
|
In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and other martingales. Quadratic variation is just one kind of variation of a process.
|
|
The theory of stochastic processes is considered to be an important contribution to mathematics and it continues to be an active topic of research for both theoretical reasons and applications.
|
|
Some particular topics of investigation are: signal transduction, gene regulatory networks, multicellular patterning, chemotaxis, systems neuroscience, the evolution of networks, and the effect of stochastic noise at the organism level.
|
|
Its applications include stochastic phenomena including heat conduction. It was first described by , and it was used by to explain results of a Bose–Einstein condensate, with proofs published by .
|
|
A subgroup of calibrated models, dynamic stochastic general equilibrium (DSGE) models are employed to represent (in a simplified way) the whole economy and simulate changes in fiscal and monetary policy.
|
|
Recently, the stochastic Dollo model is being used to analyze matrix of cognates statistically. In linguistics, this model permits a newly coined cognate to arise only once on a tree language.
|
|
In RMS 6.0, STORM’s stochastic modelling was merged with structure and fault modelling capabilities. Also introduced was the 'Workflow Manager' tool, which allows users to build and update reservoir models quickly.
|
|
Psychophysical experiments testing the thresholds of sensory systems have also been performed in humans across sensory modalities and have yielded evidence that our systems make use of stochastic resonance as well.
|
|
These works are of great significance, since they break through the framework of conventional control theory and extend the methodology and tools in the stochastic adaptive control theory to analyzing MAS.
|
|
The variations in the proportion of different color may relate to either genetic-stochastic processes. or their adaptive importance.MERRELL, D. J.,1969. Limits on heterozygous advantage as an explanation of poymorphism.
|
|
Typically, stochastic gradient descent (SGD) is used to train the network. The gradient is computed using backpropagation through structure (BPTS), a variant of backpropagation through time used for recurrent neural networks.
|
|
In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on some underlying mathematical space such as the real line, the Cartesian plane, or more abstract spaces. Point processes can be used as mathematical models of phenomena or objects representable as points in some type of space. There are different mathematical interpretations of a point process, such as a random counting measure or a random set. Some authors regard a point process and stochastic process as two different objects such that a point process is a random object that arises from or is associated with a stochastic process, though it has been remarked that the difference between point processes and stochastic processes is not clear.
|
|
A point process is a collection of points randomly located on some mathematical space such as the real line, n-dimensional Euclidean space, or more abstract spaces. Sometimes the term point process is not preferred, as historically the word process denoted an evolution of some system in time, so a point process is also called a random point field. There are different interpretations of a point process, such a random counting measure or a random set. Some authors regard a point process and stochastic process as two different objects such that a point process is a random object that arises from or is associated with a stochastic process, though it has been remarked that the difference between point processes and stochastic processes is not clear.
|
|
Stochastic quantum mechanics (or the stochastic interpretation) is an interpretation of quantum mechanics. The modern application of stochastics to quantum mechanics involves the assumption of spacetime stochasticity, the idea that the small-scale structure of spacetime is undergoing both metric and topological fluctuations (John Archibald Wheeler's "quantum foam"), and that the averaged result of these fluctuations recreates a more conventional- looking metric at larger scales that can be described using classical physics, along with an element of nonlocality that can be described using quantum mechanics. A stochastic interpretation of quantum mechanics is due to persistent vacuum fluctuation. The main idea is that vacuum or spacetime fluctuations are the reason for quantum mechanics and not a result of it as it is usually considered.
|
|
Stochastic processes may be used in music to compose a fixed piece or may be produced in performance. Stochastic music was pioneered by Xenakis, who coined the term stochastic music. Specific examples of mathematics, statistics, and physics applied to music composition are the use of the statistical mechanics of gases in Pithoprakta, statistical distribution of points on a plane in Diamorphoses, minimal constraints in Achorripsis, the normal distribution in ST/10 and Atrées, Markov chains in Analogiques, game theory in Duel and Stratégie, group theory in Nomos Alpha (for Siegfried Palm), set theory in Herma and Eonta , and Brownian motion in N'Shima. Xenakis frequently used computers to produce his scores, such as the ST series including Morsima-Amorsima and Atrées, and founded CEMAMu .
|
|
Since the market crash of 1987, it has been observed that market implied volatility for options of lower strike prices are typically higher than for higher strike prices, suggesting that volatility varies both for time and for the price level of the underlying security - a so-called volatility smile; and with a time dimension, a volatility surface. The main approach here is to treat volatility as stochastic, with the resultant Stochastic volatility models, and the Heston model as prototype; see #Risk-neutral_measure for a discussion of the logic. Other models include the CEV and SABR volatility models. One principal advantage of the Heston model, however, is that it can be solved in closed-form, while other stochastic volatility models require complex numerical methods.
|
|
In real-life data, particularly for large datasets, the notions of rough approximations were found to be excessively restrictive. Therefore, an extension of DRSA, based on stochastic model (Stochastic DRSA), which allows inconsistencies to some degree, has been introduced.Dembczyński, K., Greco, S., Kotłowski, W., Słowiński, R.: Statistical model for rough set approach to multicriteria classification. In Kok, J.N., Koronacki, J., de Mantaras, R.L., Matwin, S., Mladenic, D., Skowron, A. (eds.): Knowledge Discovery in Databases: PKDD 2007, Warsaw, Poland.
|
|
In mathematics, Doob's martingale inequality, also known as Kolmogorov’s submartingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a stochastic process exceeds any given value over a given interval of time. As the name suggests, the result is usually given in the case that the process is a martingale, but the result is also valid for submartingales. The inequality is due to the American mathematician Joseph L. Doob.
|
|
These methods rely on the hypothesis that a set of sequences share a binding motif for functional reasons. Binding motif discovery methods can be divided roughly into enumerative, deterministic and stochastic. MEME and Consensus are classical examples of deterministic optimization, while the Gibbs sampler is the conventional implementation of a purely stochastic method for DNA binding motif discovery. Another instance of this class of methods is SeSiMCMC that is focused of weak TFBS sites with symmetry.
|
|
Population-based metaheuristic are stochastic search techniques that have been successfully applied in many real and complex applications (epistatic, multimodal, multi- objective, and highly constrained problems). A population-based algorithm is an iterative technique that applies stochastic operators on a pool of individuals: the population (see the algorithm below). Every individual in the population is the encoded version of a tentative solution. An evaluation function associates a fitness value to every individual indicating its suitability to the problem.
|
|
In a 1938 paper, Kolmogorov "established the basic theorems for smoothing and predicting stationary stochastic processes"—a paper that had major military applications during the Cold War.Salsburg, p. 139. In 1939, he was elected a full member (academician) of the USSR Academy of Sciences. During World War II Kolmogorov contributed to the Russian war effort by applying statistical theory to artillery fire, developing a scheme of stochastic distribution of barrage balloons intended to help protect Moscow from German bombers.
|
|
Equivalent dose HT is used for assessing stochastic health risk due to external radiation fields that penetrate uniformly through the whole body. However it needs further corrections when the field is applied only to part(s) of the body, or non-uniformly to measure the overall stochastic health risk to the body. To enable this a further dose quantity called effective dose must be used to take into account the varying sensitivity of different organs and tissues to radiation.
|
|
The definition of separability can also be stated for other index sets and state spaces,, p. 22 such as in the case of random fields, where the index set as well as the state space can be n-dimensional Euclidean space. The concept of separability of a stochastic process was introduced by Joseph Doob,. The underlying idea of separability is to make a countable set of points of the index set determine the properties of the stochastic process.
|
|
Stratonovich invented a stochastic calculus which serves as an alternative to the Itō calculus; the Stratonovich calculus is most natural when physical laws are being considered. The Stratonovich integral appears in his stochastic calculus. Here, the Stratonovich integral is named after him (at the same time developed by Donald Fisk). He also solved the problem of optimal non-linear filtering based on his theory of conditional Markov processes, which was published in his papers in 1959 and 1960.
|
|
In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also generalizes the concepts of a Markov chain and of a subshift of finite type. The languages recognized by probabilistic automata are called stochastic languages; these include the regular languages as a subset. The number of stochastic languages is uncountable.
|
|
1551–1587 Since 2005, he has been working on statistical learning problems, including the analysis of stochastic optimization algorithms.A Garivier, E Moulines, « On upper-confidence bound policies for switching bandit problems », International Conference on Algorithmic Learning, 2011, pp. 174–188E Moulines, FR Bach, « Non-asymptotic analysis of stochastic approximation algorithms for machine learning », Advances in Neural Information Processing Systems, 2011, pp. 451–459 He joined the Centre de mathématiques appliquées de l'École polytechnique as a professor in 2015.
|
|
Mishura earned a Ph.D. in 1978 from the Taras Shevchenko National University of Kyiv with a dissertation on Limit Theorems for Functionals from Stochastic Fields supervised by Dmitrii Sergeevich Silvestrov. She earned a Dr. Sci. from the National Academy of Sciences of Ukraine in 1990 with a dissertation Martingale Methods in the Theory of Stochastic Fields. She became an assistant professor in the Faculty of Mechanics and Mathematics at National Taras Shevchenko University of Kyiv in 1976.
|
|
Daniel Leonard Ocone (born 1953) is a Professor in the Mathematics Department at Rutgers University, where he specializes in probability theory and stochastic processes.Source: Rutgers University web site He obtained his Ph.D at MIT in 1980 under the supervision of Sanjoy K. Mitter. He is known for the Clark–Ocone theorem in stochastic analysis. The continuous Ocone martingale is also named after him; it is a continuous martingale that is conditionally Gaussian, given its quadratic variation process.
|
|
Two models for hematopoiesis have been proposed: determinism and stochastic theory. For the stem cells and other undifferentiated blood cells in the bone marrow, the determination is generally explained by the determinism theory of haematopoiesis, saying that colony stimulating factors and other factors of the haematopoietic microenvironment determine the cells to follow a certain path of cell differentiation. This is the classical way of describing haematopoiesis. In stochastic theory, undifferentiated blood cells differentiate to specific cell types by randomness.
|
|
Although stochastic computing has a number of defects when considered as a method of general computation, there are certain applications that highlight its strengths. One notable case occurs in the decoding of certain error correcting codes. In developments unrelated to stochastic computing, highly effective methods of decoding LDPC codes using the belief propagation algorithm were developed. Belief propagation in this context involves iteratively reestimating certain parameters using two basic operations (essentially, a probabilistic XOR operation and an averaging operation).
|
|
Her research interests include the use of random walks to model transport in disordered media, and stochastic processes more generally. She is also interested in physical and biological applications of probability theory.
|
|
Classical theory is a GPT where states correspond to probability distributions and both measurements and physical operations are stochastic maps. One can see that in this case all state spaces are simplexes.
|
|
Springer, New York, second edition, 2008. as well as the related fields of stochastic geometry and spatial statistics,J. Moller and R. P. Waagepetersen. Statistical inference and simulation for spatial point processes.
|
|
2nd ed. Syngress Publishing; 2009. Consequently, industry demanded a new investigative technique. Since its invention, stochastic forensics has been used in real world investigation of insider data theft,Grier, Jonathan (May 2012).
|
|
F. Baccelli and B. Błaszczyszyn. Stochastic Geometry and Wireless Networks, Volume I – Theory, volume 3, No 3-4 of Foundations and Trends in Networking. NoW Publishers, 2009. F. Baccelli and B. Błaszczyszyn.
|
|
Stochastic geometry wireless models have been proposed for several network types including cognitive radio networks,T. V. Nguyen and F. Baccelli. A probabilistic model of carrier sensing based cognitive radio. In Proc.
|
|
At the same time, the use of the Ito approach leads to a stochastic evolution operator with the shifted flow vector field as compared to that of the original SDE under consideration.
|
|
The monograph Orthogonal polynomials, published in 1939, contains much of his research and has had a profound influence in many areas of applied mathematics, including theoretical physics, stochastic processes and numerical analysis.
|
|
In 2013, Busic, Fatès, Marcovici and Mairesse gave a simpler proof of the impossibility to have a perfect density classifier, which holds both for deterministic and stochastic cellular and for any dimension.
|
|
The calculus allows integration by parts with random variables; this operation is used in mathematical finance to compute the sensitivities of financial derivatives. The calculus has applications for example in stochastic filtering.
|
|
Another form of loading noise, broadband noise consists of various stochastic noise sources. Turbulence ingestion through the rotor, the rotor wake itself, and blade self-noise are each sources of broadband noise.
|
|
Springer, 1999. are ideal for sampling rough stochastic processes. Since optimal lattices, in general, are non-separable, designing interpolation and reconstruction filters requires non-tensor-product (i.e., non-separable) filter design mechanisms.
|
|
In mathematics, the Milstein method is a technique for the approximate numerical solution of a stochastic differential equation. It is named after Grigori N. Milstein who first published the method in 1974.
|
|
Stochastic resonance is a phenomenon that occurs in a threshold measurement system (e.g. a man-made instrument or device; a natural cell, organ or organism) when an appropriate measure of information transfer (signal-to-noise ratio, mutual information, coherence, d', etc.) is maximized in the presence of a non-zero level of stochastic input noise thereby lowering the response threshold; the system resonates at a particular noise level. The three criteria that must be met for stochastic resonance to occur are: # Nonlinear device or system: the input-output relationship must be nonlinear # Weak, periodic signal of interest: the input signal must be below threshold of measurement device and recur periodically # Added input noise: there must be random, uncorrelated variation added to signal of interest Stochastic resonance occurs when these conditions combine in such a way that a certain average noise intensity results in maximized information transfer. A time- averaged (or, equivalently, low-pass filtered) output due to signal of interest plus noise will yield an even better measurement of the signal compared to the system's response without noise in terms of SNR.
|
|
In statistics, econometrics and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation). Together with the moving-average (MA) model, it is a special case and key component of the more general autoregressive–moving-average (ARMA) and autoregressive integrated moving average (ARIMA) models of time series, which have a more complicated stochastic structure; it is also a special case of the vector autoregressive model (VAR), which consists of a system of more than one interlocking stochastic difference equation in more than one evolving random variable. Contrary to the moving-average (MA) model, the autoregressive model is not always stationary as it may contain a unit root.
|
|
He investigated the capability issues of robust and adaptive control in dealing with uncertainty, and revealed that to capture the intrinsic limitations of adaptive control, it is necessary to use sup-types of transient and persistent performance, rather than limsup-types which reflect only asymptotic behavior of a system. This indicates that intimate interaction and inherent conflict between identification and control result in a certain performance lower bound which does not approach the nominal performance even when the system varies very slowly. For nonlinear hybrid stochastic systems with unknown jump-Markov parameters, he with co-authors used the Wonham nonlinear filter to estimate the unknown parameters and presented an estimation error bound, which is a basic tool and plays an important role in performance analysis of adaptive control of nonlinear hybrid stochastic systems. He also attacked a series of hard problems related on global output- feedback control of nonlinear stochastic systems with inverse dynamics, including practical output-feedback risk-sensitive control, robust adaptive stabilization, small-gain theorem of general nonlinear stochastic systems.
|
|
In probability and statistics, a spherical contact distribution function, first contact distribution function,D. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. Stochastic geometry and its applications, edition 2. Wiley Chichester, 1995.
|
|
Cyrus Derman (July 16, 1925 – April 27, 2011) was an American mathematician and amateur musician who did research in Markov decision process, stochastic processes, operations research, statistics and a variety of other fields.
|
|
A number of elaborations on this basic L-system technique have been developed which can be used in conjunction with each other. Among these are stochastic grammars, context sensitive grammars, and parametric grammars.
|
|
In probability theory, the Mabinogion sheep problem or Mabinogian urn is a problem in stochastic control introduced by , who named it after a herd of magic sheep in the Welsh epic the Mabinogion.
|
|
Other important contributions concern constructive quantum field theory and representation theory of infinite dimensional groups. He also initiated a new approach to the study of galaxy and planets formation inspired by stochastic mechanics.
|
|
Finally, LISA will be sensitive to the stochastic gravitational wave background generated in the early universe through various channels, including inflation, first order phase transitions related to spontaneous symmetry breaking, and cosmic strings.
|
|
It offers a method of solving certain partial differential equations by simulating random paths of a stochastic process. Conversely, an important class of expectations of random processes can be computed by deterministic methods.
|
|
Johan Paulsson is a Swedish mathematician and systems biologist at Harvard Medical School. He is a leading researcher in systems biology and stochastic processes, specializing in stochasticity in gene networks and plasmid reproduction.
|
|
Dekel's research topics include machine learning, online prediction, statistical learning theory, and stochastic optimization. He is currently engaged in the application of machine learning techniques in the development of the Bing search engine.
|
|
Stochastic chains with memory of variable length are a family of stochastic chains of finite order in a finite alphabet, such as, for every time pass, only one finite suffix of the past, called context, is necessary to predict the next symbol. These models were introduced in the information theory literature by Jorma Rissanen in 1983, as a universal tool to data compression, but recently have been used to model data in different areas such as biology, linguistics and music.
|
|
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of gradient descent optimization, since it replaces the actual gradient (calculated from the entire data set) by an estimate thereof (calculated from a randomly selected subset of the data). Especially in high- dimensional optimization problems this reduces the computational burden, achieving faster iterations in trade for a lower convergence rate.
|
|
At Carleton University he became in 1970 an associate professor and in 1971 a professor, working in this position until 1996. From 1996 to 2000 Dawson was the director of the Fields Institute and during these years also an adjunct professor at the University of Toronto. From 2000 to 2010 he was an adjunct professor at McGill University. Dawson works on stochastic processes, measure-valued processes, and hierarchical stochastic systems with applications in information systems, genetics, evolutionary biology, and economics.
|
|
Microprocess models of decision making. Cambridge handbook of computational psychology, 302-321. The DFT has been shown to account for many puzzling findings regarding human choice behavior including violations of stochastic dominance, violations of strong stochastic transitivity, violations of independence between alternatives, serial position effects on preference, speed accuracy tradeoff effects, inverse relation between probability and decision time, changes in decisions under time pressure, as well as preference reversals between choices and prices. The DFT also offers a bridge to neuroscience.
|
|
Sir Martin Hairer (born 14 November 1975) is an Austrian-British mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at Imperial College London, having previously held appointments at the University of Warwick and the Courant Institute of New York University. In 2014 he was awarded the Fields Medal, one of the highest honours a mathematician can achieve.Daniel Saraga: The equation Tamer, in: Horizons, Swiss National Science Foundation No. 103, p.
|
|
He received his BS from Antioch College, 1977; his MS from the University of Cincinnati, 1978; and his PhD from The University of Texas at Austin under Cécile DeWitt-Morette, 1985, in the area of applying stochastic differential equations to statistical mechanics and field theory. His masters thesis was entitled: Generation of solutions to the Einstein equations. His PhD thesis was entitled, Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics.
|
|
Another method of categorising military simulations is to divide them into two broad areas. Heuristic simulations are those that are run with the intention of stimulating research and problem solving; they are not necessarily expected to provide empirical solutions. Stochastic simulations are those that involve, at least to some extent, an element of chance. Most military simulations fall somewhere in between these two definitions, although manual simulations lend themselves more to the heuristic approach and computerised ones to the stochastic.
|
|
The SABR model (Stochastic Alpha, Beta, Rho), introduced by Hagan et al.PS Hagan, D Kumar, A Lesniewski, DE Woodward (2002) Managing smile risk, Wilmott, 84-108. describes a single forward F (related to any asset e.g. an index, interest rate, bond, currency or equity) under stochastic volatility \sigma: :dF_t=\sigma_t F^\beta_t\, dW_t, :d\sigma_t=\alpha\sigma_t\, dZ_t, The initial values F_0 and \sigma_0 are the current forward price and volatility, whereas W_t and Z_t are two correlated Wiener processes (i.e.
|
|
MDA of individual cell genomes results in highly uneven genome coverage, i.e. relative overrepresentation and underrepresentation of various regions of the template, leading to loss of some sequences. There are two components to this process: a) stochastic over- and under-amplification of random regions; and b) systematic bias against high %GC regions. The stochastic component may be addressed by pooling single-cell MDA reactions from the same cell type, by employing fluorescent in situ hybridization (FISH) and/or post-sequencing confirmation.
|
|
Stochastic resonance is the term given to an instance when synaptic noise aids, rather than impairs, signal detection. With stochastic resonance, synaptic noise can amplify the recognition of signals that are below threshold potential in nonlinear, threshold-detecting systems. This is important in cells that receive and integrate thousands of synaptic inputs. These cells can often require numerous synaptic events to occur at the same time in order to produce an action potential, so the potential for receiving subthreshold signals is high.
|
|
Both fixed-source and criticality calculations can be solved using deterministic methods or stochastic methods. In deterministic methods the transport equation (or an approximation of it, such as diffusion theory) is solved as a differential equation. In stochastic methods such as Monte Carlo discrete particle histories are tracked and averaged in a random walk directed by measured interaction probabilities. Deterministic methods usually involve multi-group approaches while Monte Carlo can work with multi-group and continuous energy cross-section libraries.
|
|
Prices tend to close near the extremes of the recent range just before turning points. In the case of an uptrend, prices tend to make higher highs, and the settlement price usually tends to be in the upper end of that time period's trading range. When the momentum starts to slow, the settlement prices will start to retreat from the upper boundaries of the range, causing the stochastic indicator to turn down at or before the final price high. Stochastic divergence.
|
|
In the literature, there are two types of MPCs for stochastic systems; Robust model predictive control and Stochastic Model Predictive Control (SMPC). Robust model predictive control is a more conservative method which considers the worst scenario in the optimization procedure. However, this method, similar to other robust controls, deteriorates the overall controller's performance and also is applicable only for systems with bounded uncertainties. The alternative method, SMPC, considers soft constraints which limit the risk of violation by a probabilistic inequality.
|
|
In real-life situations, the transportation network is usually stochastic and time-dependent. In fact, a traveler traversing a link daily may experiences different travel times on that link due not only to the fluctuations in travel demand (origin-destination matrix) but also due to such incidents as work zones, bad weather conditions, accidents and vehicle breakdowns. As a result, a stochastic time-dependent (STD) network is a more realistic representation of an actual road network compared with the deterministic one.Loui, R.P., 1983.
|
|
The third parameter is restricted to the stochastic versions and is about what assumptions we can make about the distribution of the realizations and how the distribution is represented in the input. In the Stochastic Canadian Traveller Problem and in the Edge- independent Stochastic Shortest Path Problem (i-SSPPR), each uncertain edge (or cost) has an associated probability of being in the realization and the event that an edge is in the graph is independent of which other edges are in the realization. Even though this is a considerable simplification, the problem is still #P-hard. Another variant is to make no assumption on the distribution but require that each realization with non-zero probability be explicitly stated (such as “Probability 0.1 of edge set { {3,4},{1,2} }, probability 0.2 of...”).
|
|
Sergio Albeverio (born 17 January 1939) is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis (including infinite dimensional, non-standard, and stochastic analysis), mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences. He initiated (with Raphael Høegh-Krohn) a systematic mathematical theory of Feynman path integrals and of infinite dimensional Dirichlet forms and associated stochastic processes (with applications particularly in quantum mechanics, statistical mechanics and quantum field theory). He also gave essential contributions to the development of areas such as p-adic functional and stochastic analysis as well as to the singular perturbation theory for differential operators.
|
|
Cambridge university press, 2009. The underlying mathematical space of the Poisson point process is called a carrier space,E. F. Harding and R. Davidson. Stochastic geometry: a tribute to the memory of Rollo Davidson.
|
|
A stochastic control problem is one in which the evolution of the state variables is subjected to random shocks from outside the system. A deterministic control problem is not subject to external random shocks.
|
|
This still does not create a fully dynamic stochastic process with drift and noise, which allows flexible hedging and risk management. The best solutions are truly dynamic copula frameworks, see section ‘Dynamic Copulas’ below.
|
|
M. Haenggi, J. Andrews, F. Baccelli, O. Dousse, and M. Franceschetti. Stochastic geometry and random graphs for the analysis and design of wireless networks. IEEE JSAC, 27(7):1029–1046, September 2009.S. Mukherjee.
|
|
The use of stochastic geometry can then allow for the derivation of closed-form or semi-closed-form expressions for these quantities without resorting to simulation methods or (possibly intractable or inaccurate) deterministic models.
|
|
If the function is linear and can be described by a stochastic matrix, that is, a matrix whose rows or columns sum to one, then the iterated system is known as a Markov chain.
|
|
He started work on a PhD on stochastic processes with Cramér as supervisor. Away from the thesis Wold and Cramér did some joint work, their best known result being the Cramér–Wold theorem (1936).
|
|
ARCH-type models are sometimes considered to be in the family of stochastic volatility models, although this is strictly incorrect since at time t the volatility is completely pre-determined (deterministic) given previous values.
|
|
Various validated statistical models and predictors are employed which provide a platform for research in climate change. These include extreme value analysis, non-linear time series analysis, statistical downscaling, and the stochastic weather generator.
|
|
Smoluchowski presented an equation which became a basis for the theory of stochastic processes. In 1916 he proposed the equation for diffusion in an external potential field. This equation bears his name.Chandrasekhar, S. (1943).
|
|
Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics, in Pattern theory and computational vision and in option pricing.
|
|
Eilon Solan () (born 1969) is an Israeli mathematician, science fiction writer, and professor at the School of Mathematical Sciences of Tel Aviv University. His research focuses on game theory, stochastic processes, and measure theory.
|
|
The theorem is valid word by word also for stochastic processes taking values in the -dimensional Euclidean space or the complex vector space . This follows from the one-dimensional version by considering the components individually.
|
|
An introduction to the theory of point processes. Vol. {II}. Probability and its Applications (New York). Springer, New York, second edition, 2008. as well as the related fields of stochastic geometry and spatial statistics,J.
|
|
Also known as stochastic sampling, it avoids the regularity of grid supersampling. However, due to the irregularity of the pattern, samples end up being unnecessary in some areas of the pixel and lacking in others.
|
|
Stochastic analysis of spatial and opportunistic aloha. IEEE Journal on Selected Areas in Communications, 27(7):1105–1119, 2009. and then further extended to a pure or non-slotted Aloha case.B. Błaszczyszyn and P. Mühlethaler.
|
|
Another example is that \xi could be realizations of a simulation model whose outputs are stochastic. The empirical distribution of the sample could be used as an approximation to the true but unknown output distribution.
|
|
The demand and the forecast are often considered to be qualitative, limited to only two possible values: high and low. In case of stochastic demand, the uncertainty of the forecasts can also be private information.
|
|
Ordinary differential equations appear in celestial mechanics (planets, stars and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.
|
|
Books 1\. 1961: & S.E. Finer and H.B. Berrington Backbench Opinion in the House of Commons, 1955–1959. Oxford: Pergamon Press. 2\. 1967: Stochastic Models for Social Processes, New York and London: John Wiley and Sons.
|
|
An event known as "stochastic pop" occurs when prices break out and keep going. This is interpreted as a signal to increase the current position, or liquidate if the direction is against the current position.
|
|
Moreover, the EF1 guarantee holds for any cardinal utilities consistent with the ordinal ranking, i.e., it is stochastic-dominance EF1 (sd-EF1). The algorithm uses as subroutines both the PS algorithm and the Birkhoff algorithm.
|
|
One can stack the vectors in order to write a VAR(p) as a stochastic matrix difference equation, with a concise matrix notation: : Y=BZ +U \, Details of the matrices are in a separate page.
|
|
Valuation of constant maturity swaps depend on volatilities of different forward rates and therefore requires a stochastic yield curve model or some approximated methodology like a convexity adjustment, see for example Brigo and Mercurio (2006).
|
|
A. Baddeley, I. Bárány, and R. Schneider. Spatial point processes and their applications. Stochastic Geometry: Lectures given at the CIME Summer School held in Martina Franca, Italy, September 13–18, 2004, pages 1–75, 2007.
|
|
Structural BMPs are defined as the components of the drainage pathway between the source of runoff and a stormwater discharge location that affect the volume, timing, or quality of runoff. SELDM uses a simple stochastic statistical model of BMP performance to develop planning-level estimates of runoff-event characteristics. This statistical approach can be used to represent a single BMP or an assemblage of BMPs. The SELDM BMP-treatment module has provisions for stochastic modeling of three stormwater treatments: volume reduction, hydrograph extension, and water-quality treatment.
|
|
In queueing theory, a discipline within the mathematical theory of probability, a fluid limit, fluid approximation or fluid analysis of a stochastic model is a deterministic real-valued process which approximates the evolution of a given stochastic process, usually subject to some scaling or limiting criteria. Fluid limits were first introduced by Thomas G. Kurtz publishing a law of large numbers and central limit theorem for Markov chains. It is known that a queueing network can be stable, but have an unstable fluid limit.
|
|
Quantum probability was developed in the 1980s as a noncommutative analog of the Kolmogorovian theory of stochastic processes. One of its aims is to clarify the mathematical foundations of quantum theory and its statistical interpretation. A significant recent application to physics is the dynamical solution of the quantum measurement problem, by giving constructive models of quantum observation processes which resolve many famous paradoxes of quantum mechanics. Some recent advances are based on quantum filtering and feedback control theory as applications of quantum stochastic calculus.
|
|
In supersymmetric theory of SDEs, the finite-time stochastic evolution operator is given its most natural mathematical meaning of the stochastically averaged pullback induced on the exterior algebra of the phase space by the noise-configuration- dependent SDE-defined diffeomorphisms. This operator is unique and corresponds to the Stratonovich interpretation of SDEs. In addition, Stratonovich approach is equivalent to the Weyl symmetrization convention needed for disambiguation of the stochastic evolution operator during the transition from path integral to its operator representation. Moreover, in the appendix of Ref.
|
|
For large noise intensities, the output is dominated by the noise, also leading to a low signal-to-noise ratio. For moderate intensities, the noise allows the signal to reach threshold, but the noise intensity is not so large as to swamp it. Thus, a plot of signal-to-noise ratio as a function of noise intensity contains a peak. Strictly speaking, stochastic resonance occurs in bistable systems, when a small periodic (sinusoidal) force is applied together with a large wide band stochastic force (noise).
|
|
Let X1, X2, ... be an infinite sequence of independent and identically distributed random variables. The initial rank of the nth term of this sequence is the value r such that for exactly r values of i less than or equal to n. Let denote the stochastic process consisting of the terms Xi having initial rank k; that is, Yk,j is the jth term of the stochastic process that achieves initial rank k. The sequence Yk is called the sequence of kth partial records.
|
|
The idea of adding noise to a system in order to improve the quality of measurements is counter-intuitive. Measurement systems are usually constructed or evolved to reduce noise as much as possible and thereby provide the most precise measurement of the signal of interest. Numerous experiments have demonstrated that, in both biological and non-biological systems, the addition of noise can actually improve the probability of detecting the signal; this is stochastic resonance. The systems in which stochastic resonance occur are always nonlinear systems.
|
|
Almost surely, a sample path of a Wiener process is continuous everywhere but nowhere differentiable. It can be considered as a continuous version of the simple random walk. The process arises as the mathematical limit of other stochastic processes such as certain random walks rescaled, which is the subject of Donsker's theorem or invariance principle, also known as the functional central limit theorem. The Wiener process is a member of some important families of stochastic processes, including Markov processes, Lévy processes and Gaussian processes.
|
|
Di Nunno earned a degree in mathematics from the University of Milan in 1998, including research on stochastic functions with Yurii Rozanov. She moved to the University of Pavia for doctoral studies, continuing with Rozanov as an informal mentor but under the official supervision of Eugenio Regazzini. She completed her Ph.D. in 2003; her dissertation was On stochastic differentiation with applications to minimal variance hedging. She joined the University of Oslo in 2003, and added her affiliation with the Norwegian School of Economics in 2009.
|
|
Prior integrate-and-fire models with stochastic characteristics relied on including a noise to simulate stochasticity. The Galves–Löcherbach model distinguishes itself because it is inherently stochastic, incorporating probabilistic measures directly in the calculation of spikes. It is also a model that may be applied relatively easily, from a computational standpoint, with a good ratio between cost and efficiency. It remains a non-Markovian model, since the probability of a given neuronal spike depends on the accumulated activity of the system since the last spike.
|
|
The content of the theory is effectively that of invariant (smooth) measures on (preferably compact) homogeneous spaces of Lie groups; and the evaluation of integrals of the differential forms.Luis Santaló (1976) Integral Geometry and Geometric Probability, Addison Wesley A very celebrated case is the problem of Buffon's needle: drop a needle on a floor made of planks and calculate the probability the needle lies across a crack. Generalising, this theory is applied to various stochastic processes concerned with geometric and incidence questions. See stochastic geometry.
|
|
Francis, A., "Limitations of Deterministic and Advantages of Stochastic Seismic Inversion", CSEG Records, February 2005, p. 5-11. Geostatistical inversion procedures detect and delineate thin reservoirs otherwise poorly defined.Merletti, G., Torres-Verdin, C., "Accurate Detection and Spatial Delineation of Thin-Sand Sedimentary Sequences via Joint Stochastic Inversion of Well Logs and 3D Pre-Stack Seismic Amplitude Data", SPE 102444. Markov chain Monte Carlo (MCMC) based geostatistical inversion addresses the vertical scaling problem by creating seismic derived rock properties with vertical sampling compatible to geologic models.
|
|
Pliska–Pinheiro–Pinto Optimization paper determined the optimal life insurance purchase in a continuous-time model where the individual's lifetime is modeled through the concept of uncertain lifetime found in reliability theory. Pinto–Pinheiro–Yannacopoulos's JDEA paper study price formation in the Arrow–Debreu financial models with multiple assets from an unconventional perspective using Edgeworthian exchange models. Pinto–Pinheiro–Yannacopoulos's JDEA paper develops a stochastic model for the dynamics of bargaining. Araujo–-Choubdar-Maldonado–Pinheiro–Pinto proved the stochastic stability of sunspot equilibria in some specific cases.
|
|
The mathematical algorithm for the wave propagation is based on a stochastic model and pre recorded signal envelope. Multipath propagation is achieved by inducing multiple simulated electromagnetic paths digitally thus producing signal fading and audio distortion.
|
|
Because the motor events are stochastic, molecular motors are often modeled with the Fokker–Planck equation or with Monte Carlo methods. These theoretical models are especially useful when treating the molecular motor as a Brownian motor.
|
|
Jean-Pierre Florens (born 6 July 1947) is an influential French econometrician at Toulouse School of Economics. He is known for his research on Bayesian inference, econometrics of stochastic processes, causality, frontier estimation, and inverse problems.
|
|
His research interests include several areas of probability theory, Finitely addtive probability measures, stochastic calculus, martingale problems and Markov processes, Filtering theory, option pricing theory, psephology in the context of Indian elections and cryptography, among others.
|
|
A general drawback of stochastic simulations is that for big systems, too many events happen which cannot all be taken into account in a simulation. The following methods can dramatically improve simulation speed by some approximations.
|
|
Sampled differential dynamic programming has been extended to Path Integral Policy Improvement with Differential Dynamic Programming. This creates a link between differential dynamic programming and path integral control, which is a framework of stochastic optimal control.
|
|
The claims arising from policies or portfolios that the company has written can also be modelled using stochastic methods. This is especially important in the general insurance sector, where the claim severities can have high uncertainties.
|
|
The ion beam emittance may be decreased via various methods of beam cooling, such as electron cooling or stochastic cooling. In addition, one must consider the effect of intrabeam scattering, which is largely a heating effect.
|
|
Stochastic dynamic programming is frequently used to model animal behaviour in such fields as behavioural ecology.Mangel, M. & Clark, C. W. 1988. Dynamic modeling in behavioral ecology. Princeton University Press Houston, A. I & McNamara, J. M. 1999.
|
|
The role of genetic drift by means of sampling error in evolution has been criticized by John H. Gillespie and William B. Provine, who argue that selection on linked sites is a more important stochastic force.
|
|
"Digital Forensics Magazine." Grier is a frequent speaker at computer conferences such as Black Hat, ACSAC, and DFRWS.Black Hat Briefings, USA 2012.Catching Insider Data Theft with Stochastic Forensics .ACSAC,. ACSAC 2012 Program.ACSAC, ACSAC 2011 Program.
|
|
Ecorithms and fuzzy logic also have the common property of dealing with possibilities more than probabilities, although feedback and feed forward, basically stochastic weights, are a feature of both when dealing with, for example, dynamical systems.
|
|
A measure is said to be s-finite if it is a countable sum of bounded measures. S-finite measures are more general than sigma-finite ones and have applications in the theory of stochastic processes.
|
|
In mathematics, Hörmander's condition is a property of vector fields that, if satisfied, has many useful consequences in the theory of partial and stochastic differential equations. The condition is named after the Swedish mathematician Lars Hörmander.
|
|
131, pp. 373-395, 2004. showed that COAC-type algorithms could be assimilated methods of stochastic gradient descent, on the cross-entropy and estimation of distribution algorithm. They proposed these metaheuristics as a "research-based model".
|
|
In addition to the discrete dominant periods, small-amplitude stochastic variations are seen. It is proposed that this is due to granulation, similar to the same effect on the sun but on a much larger scale.
|
|
Maria Deijfen (born 1975) is a Swedish mathematician known for her research on random graphs and stochastic processes on graphs, including the Reed–Frost model of epidemics. She is a professor of mathematics at Stockholm University.
|
|
Characterization of Neural Responses with Stochastic Stimuli in (Ed. M. Gazzaniga) The Cognitive Neurosciences 3rd edn (pp 327–338) MIT press.Schwartz O., Pillow J. W., Rust N. C., & Simoncelli E. P. (2006). Spike- triggered neural characterization.
|
|
Komboï (, Knots) is a 1981 stochastic composition for amplified harpsichord and percussion by Greek composer Iannis Xenakis. It is one of the two compositions for harpsichord and percussion written by Xenakis, the other one being Oophaa.
|
|
Another example of violation of probabilistic bounds is provided by the famous Bell's inequality: entangled states exhibit a form of stochastic dependence stronger than the strongest classical dependence: and in fact they violate Fréchet like bounds.
|
|
Anatol Rapoport Anatol Rapoport (; ; May 22, 1911January 20, 2007) was an American mathematical psychologist. He contributed to general systems theory, to mathematical biology and to the mathematical modeling of social interaction and stochastic models of contagion.
|
|
The time scale of the stochastic process may be calendar or clock time or some more operational measure of time progression, such as mileage of a car, accumulated wear and tear on a machine component or accumulated exposure to toxic fumes. In many applications, the stochastic process describing the system state is latent or unobservable and its properties must be inferred indirectly from censored time-to-event data and/or readings taken over time on correlated processes, such as marker processes. The word ‘regression’ in threshold regression refers to first-hitting-time models in which one or more regression structures are inserted into the model in order to connect model parameters to explanatory variables or covariates. The parameters given regression structures may be parameters of the stochastic process, the threshold state and/or the time scale itself.
|
|
Stochastic (partial) differential equations (SDEs) are the foundation for models of everything in nature above the scale of quantum degeneracy and coherence and are essentially Witten-type TQFTs. All SDEs possess topological or BRST supersymmetry, \delta, and in the operator representation of stochastic dynamics is the exterior derivative, which is naturally commutative with the stochastic evolution operator, defined as the pullback induced by phase space diffeomorphisms as specified by the SDEs and averaged over noise configurations. This supersymmetry preserves the continuity of phase space by continuous flows, and the phenomenon of supersymmetric spontaneous breakdown by a global non- supersymmetric ground state encompasses such well-established physical concepts as chaos, turbulence, 1/f and crackling noises, self-organized criticality etc. The topological sector of the theory for any SDE can be recognized as a Witten-type TQFT.
|
|
Peter George Harrison (born 1951) is a Professor of Computing Science at Imperial College London known for the reversed compound agent theorem, which gives conditions for a stochastic network to have a product-form solution. Harrison attended Christ's College, Cambridge, where he was a Wrangler in Mathematics (1972) and gained a Distinction in Part III of the Mathematical Tripos (1973), winning the Mayhew Prize for Applied Mathematics. After spending two years in industry, Harrison moved to Imperial College, London where he has worked since, obtaining his Ph.D. in Computing Science in 1979 with a thesis titled "Representative queueing network models of computer systems in terms of time delay probability distributions" and lecturing since 1983. Current research interests include parallel algorithms, performance engineering, queueing theory, stochastic models and stochastic process algebra, particularly the application of RCAT to find product-form solutions.
|
|
He is one of the namesakes of the Freidlin–Wentzell theorem in the large deviations theory of stochastic processes,. and has also used probability theory to solve partial differential equations. Friedlin was born in 1938 in Moscow.
|
|
EURANDOM He is author of the book "Large deviations for Gaussian queues", and is associate editor of the journals Stochastic Models and Queuing Systems. He contributed to the book Queues and Lévy fluctuation theory, published in 2015.
|
|
Slutsky's later work was principally in probability theory and the theory of stochastic processes. He is generally credited for the result known as Slutsky's theorem. In 1928 he was an Invited Speaker of the ICM in Bologna.
|
|
F. Baccelli and B. Błaszczyszyn. Stochastic Geometry and Wireless Networks, Volume I – Theory, volume 3, No 3–4 of Foundations and Trends in Networking. NoW Publishers, 2009. particles colliding into a detector, or trees in a forest.
|
|
This process can be defined as a sum of squared Ornstein–Uhlenbeck process. The CIR is an ergodic process, and possesses a stationary distribution. The same process is used in the Heston model to model stochastic volatility.
|
|
The less stable the pattern, the longer it should take to return to the established pattern. HKB predicts critical slowing down.Schöner, G., Haken, H., & Kelso, J.A.S. (1986). A stochastic theory of phase transitions in human hand movement.
|
|
Girsanov's theorem is important in the general theory of stochastic processes since it enables the key result that if Q is an absolutely continuous measure with respect to P then every P-semimartingale is a Q-semimartingale.
|
|
Rather than considering the distribution of all possible stochastic outcomes for given values of t, \lambda and \mu it is also possible to consider what happens when certain conditions of survivorship are imposed on the possible outcomes.
|
|
Optimal sampling lattices have been studied in higher dimensions. Generally, optimal sphere packing lattices are ideal for sampling smooth stochastic processes while optimal sphere covering latticesJ. H. Conway, N. J. A. Sloane. Sphere packings, lattices and groups.
|
|
Market power and market concentration can be estimated or quantified using several different tools and measurements, including the Lerner index, stochastic frontier analysis, and New Empirical Industrial Organization (NEIO) modeling, as well as the Herfindahl-Hirschman index.
|
|
Wall protecting worker from primary beam whilst allowing visual communication with patient. Exposure to radiation can result in harm, categorised as either deterministic or stochastic. Deterministic effects occur above a certain threshold of radiation e.g. burns, cataracts.
|
|
The Brownian motion can be modeled by a random walk. Random walks in porous media or fractals are anomalous. In the general case, Brownian motion is a non-Markov random process and described by stochastic integral equations.
|
|
Among stochastic models that are used for long-range dependence, some popular ones are autoregressive fractionally integrated moving average models, which are defined for discrete-time processes, while continuous-time models might start from fractional Brownian motion.
|
|
Others classes of stochastic hybrid simulations concern reaction–diffusion simulations M. B. Flegg, S. J. Chapman and R. Erban, The two-regime method for optimizing stochastic reaction–diffusion simulations, J. Royal. Soc. Inter. 9 (2011), 859-868.. These algorithm are used to study the conversion of species and allow to couple the Fokker-Planck equation to simulate population and single trajectories using Brownian simulations B. Franz, M. B. Flegg, S. J. Chapman and R. Erban, Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics, SIAM J. Appl. Math. 73 (2013), 1224-1247..
|
|
The equations are difficult to solve analytically, so simulations on the computer are performed as kinetic Monte Carlo schemes. The simulation is commonly carried out with the Gillespie algorithm, which uses reaction constants that are derived from chemical kinetic rate constants to predict whether a reaction is going to occur. Stochastic simulations are more computationally demanding and therefore the size and scope of the model is limited. The stochastic simulation was used to show that the Ras protein, which is a crucial signalling molecule in T cells, can have an active and inactive form.
|
|
In the early 20th century, actuaries were developing techniques that can be found in modern financial theory, but for various historical reasons, these developments did not achieve much recognition. In the late 1980s and early 1990s, there was a distinct effort for actuaries to combine financial theory and stochastic methods into their established models. In the 21st century, the profession, both in practice and in the educational syllabi of many actuarial organizations, combines tables, loss models, stochastic methods, and financial theory, but is still not completely aligned with modern financial economics.
|
|
In queueing theory, a discipline within the mathematical theory of probability, a fluid queue (fluid model, fluid flow model or stochastic fluid model) is a mathematical model used to describe the fluid level in a reservoir subject to randomly determined periods of filling and emptying. The term dam theory was used in earlier literature for these models. The model has been used to approximate discrete models, model the spread of wildfires, in ruin theory and to model high speed data networks. The model applies the leaky bucket algorithm to a stochastic source.
|
|
The general theory and techniques of stochastic geometry and, in particular, point processes have often been motivated by the understanding of a type of noise that arises in electronic systems known as shot noise. For certain mathematical functions of a point process, a standard method for finding the average (or expectation) of the sum of these functions is Campbell's formulaA. Baddeley, I. Barany, and R. Schneider. Spatial point processes and their applications. Stochastic Geometry: Lectures given at the CIME Summer School held in Martina Franca, Italy, September 13–18, 2004, pages 1–75, 2007.
|
|
An important task in stochastic geometry network models is choosing a mathematical model for the location of the network nodes. The standard assumption is that the nodes are represented by (idealized) points in some space (often Euclidean Rn, and even more often in the plane R2), which means they form a stochastic or random structure known as a (spatial) point process. According to one statistical study, the locations of cellular or mobile phone base stations in the Australian city of Sydney resemble a realization of a Poisson point process.C.-H. Lee, C.-Y.
|
|
For further reading of stochastic geometry wireless network models, see the textbook by Haenggi, the two-volume text by Baccelli and Błaszczyszyn (available online), and the survey article. For interference in wireless networks, see the monograph on interference by Ganti and Haenggi (available online). For an introduction to stochastic geometry and spatial statistics in a more general setting, see the lectures notes by Baddeley (available online with Springer subscription). For a complete and rigorous treatment of point processes, see the two-volume text by Daley and Vere-JonesD.
|
|
Mercurio worked during his Ph.D. on incomplete markets theory using dynamic mean-variance hedging techniques. With Damiano Brigo (2002–2003), he has shown how to construct stochastic differential equations consistent with mixture models, applying this to volatility smile modeling in the context of local volatility models. He is also one of the main authors in inflation modeling. Mercurio has also authored several publications in top journals and co-authored the book Interest rate models: theory and practice for Springer- Verlag, that quickly became an international reference for stochastic dynamic interest rate modeling.
|
|
Others consider a point process as a stochastic process, where the process is indexed by sets of the underlying space on which it is defined, such as the real line or n-dimensional Euclidean space. Other stochastic processes such as renewal and counting processes are studied in the theory of point processes. Sometimes the term "point process" is not preferred, as historically the word "process" denoted an evolution of some system in time, so point process is also called a random point field. Point processes are well studied objects in probability theoryKallenberg, O. (1986).
|
|
Muirhead's inequality states that [a] ≤ [b] for all x such that xi > 0 for every i ∈ { 1, ..., n } if and only if there is some doubly stochastic matrix P for which a = Pb. Furthermore, in that case we have [a] = [b] if and only if a = b or all xi are equal. The latter condition can be expressed in several equivalent ways; one of them is given below. The proof makes use of the fact that every doubly stochastic matrix is a weighted average of permutation matrices (Birkhoff-von Neumann theorem).
|
|
The Dryden wind turbulence model, also known as Dryden gusts, is a mathematical model of continuous gusts accepted for use by the United States Department of Defense in certain aircraft design and simulation applications. The Dryden model treats the linear and angular velocity components of continuous gusts as spatially varying stochastic processes and specifies each component's power spectral density. The Dryden wind turbulence model is characterized by rational power spectral densities, so exact filters can be designed that take white noise inputs and output stochastic processes with the Dryden gusts' power spectral densities.
|
|
Two types of measurements of stochastic resonance were conducted. The first, like the crayfish experiment, consisted of a pure tone pressure signal at 23 Hz in a broadband noise background of varying intensities. A power spectrum analysis of the signals yielded maximum SNR for a noise intensity equal to 25 times the signal stimulus resulting in a maximum increase of 600% in SNR. 14 cells in 12 animals were tested, and all showed an increased SNR at a particular level of noise, meeting the requirements for the occurrence of stochastic resonance.
|
|
A stochastic or random process can be defined as a collection of random variables that is indexed by some mathematical set, meaning that each random variable of the stochastic process is uniquely associated with an element in the set. The set used to index the random variables is called the index set. Historically, the index set was some subset of the real line, such as the natural numbers, giving the index set the interpretation of time. Each random variable in the collection takes values from the same mathematical space known as the state space.
|
|
The Poisson process is a stochastic process that has different forms and definitions. It can be defined as a counting process, which is a stochastic process that represents the random number of points or events up to some time. The number of points of the process that are located in the interval from zero to some given time is a Poisson random variable that depends on that time and some parameter. This process has the natural numbers as its state space and the non-negative numbers as its index set.
|
|
Stochastic quantum mechanics can be applied to the field of electrodynamics and is called stochastic electrodynamics (SED). SED differs profoundly from quantum electrodynamics (QED) but is nevertheless able to account for some vacuum- electrodynamical effects within a fully classical framework. In classical electrodynamics it is assumed there are no fields in the absence of any sources, while SED assumes that there is always a constantly fluctuating classical field due to zero-point energy. As long as the field satisfies the Maxwell equations there is no a priori inconsistency with this assumption.
|
|
Sometimes it is this restricted model that is called the stochastic block model. The case where p > q is called an assortative model, while the case p < q is called disassortative. Returning to the general stochastic block model, a model is called strongly assortative if P_{ii} > P_{jk} whenever j eq k: all diagonal entries dominate all off-diagonal entries. A model is called weakly assortative if P_{ii} > P_{ij} whenever i eq j: each diagonal entry is only required to dominate the rest of its own row and column.
|
|
At the time, it attracted the attention of André Lichnerowicz, then engaged in studies at the University of Lyon. It found some use in a variety of unforeseen applications: stochastic poetry, stochastic art, colour classification, aleatory music, architectural symbolism, etc. The notational system directly and logically encodes the binary representations of the digits in a hexadecimal (base sixteen) numeral. In place of the Arabic numerals 0–9 and letters A–F currently used in writing hexadecimal numerals, it presents sixteen newly devised symbols (thus evading any risk of confusion with the decimal system).
|
|
David Anderson provides a timely survey of the wide array of methods and techniques that can be employed to analyze stochastic models of chemical reaction networks. Such models are frequently encountered in the rapidly growing field of Systems Biology. Mindful of the interdisciplinary nature of the research community in this field, the authors present the material in such a way that it is accessible to anyone who is familiar with the standard undergraduate mathematics curriculum. # Large Deviations for Stochastic Processes (American Mathematical Society 2006): This book with his former Ph.D. student Prof.
|
|
Albeverio's main research interests include probability theory (stochastic processes; stochastic analysis; SPDEs); analysis (functional and infinite dimensional, non-standard, p-adic); mathematical physics (classical and quantum, in particular hydrodynamics, statistical physics, quantum field theory, quantum information, astrophysics); geometry (differential, non-commutative); topology (configuration spaces, knot theory); operator algebras, spectral theory; dynamical systems, ergodic theory, fractals; number theory (analytic, p-adic); representation theory; algebra; information theory and statistics; applications of mathematics in biology, earth sciences, economics, engineering, physics, social sciences, models for urban systems; epistemology, philosophical and cultural issues.
|
|
In physics, a Langevin equation (named after Paul Langevin) is a stochastic differential equation describing the time evolution of a subset of the degrees of freedom. These degrees of freedom typically are collective (macroscopic) variables changing only slowly in comparison to the other (microscopic) variables of the system. The fast (microscopic) variables are responsible for the stochastic nature of the Langevin equation. One application is to Brownian motion, calculating the statistics of the random motion of a small particle in a fluid due to collisions with the surrounding molecules in thermal motion.
|
|
Previous Granger-causality methods could only operate on continuous-valued data so the analysis of neural spike train recordings involved transformations that ultimately altered the stochastic properties of the data, indirectly altering the validity of the conclusions that could be drawn from it. In 2011, however, a new general- purpose Granger-causality framework was proposed that could directly operate on any modality, including neural-spike trains. Neural spike train data can be modeled as a point-process. A temporal point process is a stochastic time- series of binary events that occurs in continuous time.
|
|
In mathematics, an ambit field is a d-dimensional random field describing the stochastic properties of a given system. The input is in general a d-dimensional vector (e.g. d-dimensional space or (1-dimensional) time and (d − 1)-dimensional space) assigning a real value to each of the points in the field. In its most general form, the ambit field, Y, is defined by a constant plus a stochastic integral, where the integration is done with respect to a Lévy basis, plus a smooth term given by an ordinary Lebesgue integral.
|
|
Non-divergent wind fields are produced by a procedure based on the variational principle and a finite-element discretization. The dispersion model, LODI, solves the 3-D advection-diffusion equation using a Lagrangian stochastic, Monte Carlo method.Ermak, D.L., and J.S. Nasstrom (2000), A Lagrangian Stochastic Diffusion Method for Inhomogeneous Turbulence, Atmospheric Environment, 34, 7, 1059-1068. LODI includes methods for simulating the processes of mean wind advection, turbulent diffusion, radioactive decay and production, bio-agent degradation, first-order chemical reactions, wet deposition, gravitational settling, dry deposition, and buoyant/momentum plume rise.
|
|
At small scales, and with large quantities of modules, deterministic control over reconfiguration of individual modules will become unfeasible, while stochastic mechanisms will naturally prevail. Microscopic size of modules will make the use of electromagnetic actuation and interconnection prohibitive, as well, as the use of on-board power storage. Three large scale prototypes were built in attempt to demonstrate dynamically programmable three-dimensional stochastic reconfiguration in a neutral-buoyancy environment. The first prototype used electromagnets for module reconfiguration and interconnection. The modules were 100 mm cubes and weighed 0.81 kg.
|
|
Practical application of the numerical optimization results is difficult because any complex technical system is a stochastic system and the characteristics of this system have probabilistic nature. We would like to emphasize that, speaking about the stochastic properties of a technical system within the frame of optimization tasks, we imply that the important parameters of any system are stochastically spread. Normally it occurs during the production stage despite of the up-to-date level of modern technology. Random deviations of the system parameters lead to a random change in system efficiency.
|
|
Relatedly, he also believes that universities are better at public relations and claiming credit than generating knowledge. He argues that knowledge and technology are usually generated by what he calls "stochastic tinkering" rather than by top-down directed research,Nassim Nicholas Taleb, 2001, The Birth of Stochastic Science , at Edge (online), September 11, 2001, accessed 7 May 2015.Ma'n Barāzī, 2009, Lebanon's rational fools: From the roots of the "economic qabaday" till the 2009 depression election… conflicting tale of paradigms and economic change, Beirut, Lebanon:Data & Investment Consult-Lebanon, p. 182, accessed 7 May 2015.
|
|
A row (column) stochastic matrix is a square matrix each of whose rows (columns) consists of non-negative real numbers whose sum is unity. The theorem cannot be applied directly to such matrices because they need not be irreducible. If A is row-stochastic then the column vector with each entry 1 is an eigenvector corresponding to the eigenvalue 1, which is also ρ(A) by the remark above. It might not be the only eigenvalue on the unit circle: and the associated eigenspace can be multi- dimensional.
|
|
Since the gradients of V(\cdot, \cdot) in the incremental gradient descent iterations are also stochastic estimates of the gradient of I_n[w], this interpretation is also related to the stochastic gradient descent method, but applied to minimize the empirical risk as opposed to the expected risk. Since this interpretation concerns the empirical risk and not the expected risk, multiple passes through the data are readily allowed and actually lead to tighter bounds on the deviations I_n[w_t] - I_n[w^\ast_n], where w^\ast_n is the minimizer of I_n[w].
|
|
Theodore Edward Harris (11 January 1919 - 3 November 2005) was an American mathematician known for his research on stochastic processes, including such areas as general state-space Markov chains (often now called Harris chains), the theory of branching processes and stochastic models of interacting particle systems such as the contact process. The Harris inequality in statistical physics and percolation theory is named after him. He received his Ph.D. at Princeton University in 1947 under advisor Samuel Wilks. From 1947 until 1966 he worked for the RAND Corporation, heading their mathematics department from 1959 to 1965.
|
|
Bartlett left ICI for the University of Cambridge in 1938 but at the outset of World War II was mobilised into the Ministry of Supply, conducting rocket research alongside Frank Anscombe, David Kendall and Pat Moran. After the war Bartlett's renewed Cambridge work focused on time-series analysis and stochastic process. With Jo Moyal he planned a large book on probability, but the collaboration did not work out and Bartlett went ahead and published his own book on stochastic processes. He made a number of visits to the United States.
|
|
In the period 1966-1980 Meyer organised the Seminaire de Probabilities in Strasbourg, and he and his co- workers developed what is called the general theory of processes. This theory was concerned with the mathematical foundations of the theory of continuous time stochastic processes, especially Markov processes. Notable achievements of the 'Strasbourg School' were the development of stochastic integrals for semimartingales, and the concept of a predictable (or previsible) process. IRMA created an annual prize in his memory; the first Paul André Meyer prize was awarded in 2004 .
|
|
In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov at the beginning of the 20th century, and has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics.
|
|
Stéphan Fauve's work has focused mainly on non-linear physics. His thesis work focused on the study of various scenarios of transition to chaos, in particular the measurement of critical exponents associated with the cascade of period doubling.A. Libchaber, C. Laroche and S. Fauve, « Period doubling cascade in mercury, a quantitative measurement », J. Physique Lettres, 43, (1982), p. 211 He then carried out the first experiment to highlight the phenomenon of stochastic resonance.S. Fauve and F. Heslot, « Stochastic resonance in a bistable system », Physics Letters, 97a, (1983), p.
|
|
For a fixed configuration of noise, SDE has a unique solution differentiable with respect to the initial condition. Nontriviality of stochastic case shows up when one tries to average various objects of interest over noise configurations. In this sense, an SDE is not a uniquely defined entity when noise is multiplicative and when the SDE is understood as a continuous time limit of a stochastic difference equation. In this case, SDE must be complemented by what is known as "interpretations of SDE" such as Itô or a Stratonovich interpretations of SDEs.
|
|
The parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving average model). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure. Methods of time series analysis may also be divided into linear and non-linear, and univariate and multivariate.
|
|
Based on these samples, which are evaluated by the solver similarly as in the sensitivity analysis, the statistical properties of the model responses as mean value, standard deviation, quantiles and higher order stochastic moments are estimated. Reliability analysis: Within the framework of probabilistic safety assessment or reliability analysis, the scattering influences are modelled as random variables, which are defined by distribution type, stochastic moments and mutual correlations. The result of the analysis is the complementary of reliability, the probability of failure, which can be represented on a logarithmic scale.
|
|
The first is derived from applying set theory to time-point sequences, each of which is then assigned to a specific pitch. This is the configuration type the work starts with. The second type is generated by stochastic methods, arborescences constitute the third, and finally, the fourth configuration type is silence . According to this classification, there are fifty segments overall in Evryali: 23 for time-point sequences, 4 for stochastic material (appearing only at two points in the work, both times as consecutive pairs), 20 for arborescences, and 3 are silences.
|
|
Ergodic Processing involves sending a stream of bundles, which captures the benefits of regular stochastic and bundle processing. Burst Processing encodes a number by a higher base increasing stream. For instance, we would encode 4.3 with ten decimal digits as ::: 4444444555 since the average value of the preceding stream is 4.3. This representation offers various advantages: there is no randomization since the numbers appear in increasing order, so the PRNG issues are avoided, but many of the advantages of stochastic computing are retained (such as partial estimates of the solution).
|
|
Arthur James Krener (born October 8, 1942) is a Distinguished Visiting Professor in the Department of Applied Mathematics at the Naval Postgraduate School. He has made contributions in the areas of control theory, nonlinear control , and stochastic processes.
|
|
Xavier Fernique Xavier Fernique (3 May 1934 – 15 March 2020) was a mathematician, noted mostly for his contributions to the theory of stochastic processes. Fernique's theorem, a result on the integrability of Gaussian measures, is named after him.
|
|
The most vulnerable part of the evolutionary rescue process, theoretically, should be the time point during which the population is beyond the stochastic threshold, which exposes the population to random outcomes not determined by genetic or evolutionary mechanisms.
|
|
The first category is mainly based on the Epidemic models Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p42. where the pioneering research engaging rumor propagation under these models started during the 1960s.
|
|
If two variables have the same mean, they can still be compared by how "spread out" their distributions are. This is captured to a limited extent by the variance, but more fully by a range of stochastic orders.
|
|
Entangled states exhibit a form of stochastic dependence stronger than the strongest classical dependence and in fact they violate Fréchet like bounds. It is also worth mentioning that is possible to give a Bayesian interpretation of these bounds.
|
|
The mathematical object consisting of the union of all these disks is known as a Boolean (random disk) modelD. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. Stochastic geometry and its applications, volume 2. Wiley Chichester, 1995.
|
|
"Stochastic model for the multiple generation of hadrons.", OSTI, Potupa, A.S., April 1, 1974."New scaling in the pionization region of inclusive pp collision spectra at high energies.", OSTI, Potupa, A.S. ; Skadorov, V.V. ; Fridman, A.S., May 5, 1976.
|
|
Personality traits demonstrate moderate levels of continuity, smaller but still significant normative or mean-level changes, and individual differences in change, often late into the life course. This pattern is influenced by genetic, environmental, transactional, and stochastic factors.
|
|
Stochastic simulation based on emulated protocol stacks and traffic theory are the main analysis methods. Essential results of ComNets' work have been incorporated into the standards ETSI-GPRS, CEN-DSRC, ETSI/HiperLAN/2, IEEE 802.11 e/h/s.
|
|
This theorem, which is an existence theorem for measures on infinite product spaces, says that if any finite- dimensional distributions satisfy two conditions, known as consistency conditions, then there exists a stochastic process with those finite- dimensional distributions.
|
|
Anand Plappally, Alfred Soboyejo, Norman Fausey, Winston Soboyejo and Larry Brown,"Stochastic Modeling of Filtrate Alkalinity in Water Filtration Devices: Transport through Micro/Nano Porous Clay Based Ceramic Materials " J Nat Env Sci 2010 1(2):96-105.
|
|
Myatt, D.M., Bishop, J.M., Nasuto, S.J., (2004), Minimum stable convergence criteria for Stochastic Diffusion Search, Electronics Letters, 22:40, pp. 112-113. Recent work has involved merging the global search properties of SDS with other swarm intelligence algorithms.
|
|
Methods of modelling the volatility smile include stochastic volatility models and local volatility models. For a discussion as to the various alternate approaches developed here, see Financial economics#Challenges and criticism and Black–Scholes model#The volatility smile.
|
|
Rolf Georg Schneider (born 17 March 1940, Hagen, Germany)Lebens- und Karrieredaten Kürschner Gelehrtenkalender 2009 is a mathematician. Schneider is a professor emeritus at the University of Freiburg. His main research interests are convex geometry and stochastic geometry.
|
|
Point processes are employed in other mathematical and statistical disciplines, hence the notation may be used in fields such stochastic geometry, spatial statistics or continuum percolation theory, and areas which use the methods and theory from these fields.
|
|
He attended Bingley Grammar School before received a BSc in Applied Physics and Electronics (1987) and a PhD in (1991), under Peter V. E. McClintock, at Lancaster University, UK, with a thesis entitled Experiments in Stochastic Nonlinear Dynamics.
|
|
Stochastic regression shows much less bias than the above-mentioned techniques, but it still missed one thing – if data are imputed then intuitively one would think that more noise should be introduced to the problem than simple residual variance.
|
|
Chickowski, Ericka (June 26, 2012). "New Forensics Method May Nab Insider Thieves". Dark Reading. Unlike traditional computer forensics, which relies on digital artifacts, stochastic forensics does not require artifacts and can therefore recreate activity which would otherwise be invisible.
|
|
He completed his doctoral studies, "A Stochastic Approach to Describing Geological Systems" at the University of Cambridge under the supervision of Sam Edwards in 1995. Whilst at Cambridge he was part of a Group to Encourage Ethnic Minority Applicants.
|
|
Hilbert spaces are of fundamental importance in many areas, including the mathematical formulation of quantum mechanics, stochastic processes, and time-series analysis. Besides studying spaces of functions, functional analysis also studies the continuous linear operators on spaces of functions.
|
|
G. W. Hoffmann (1975) The Stochastic Theory of the Origin of the Genetic Code. Annu. Rev. Phys. Chem. 26, 123-144 (H. Eyring, Ed.) These calculations support the view that the origin of replication and metabolism together is plausible.
|
|
Introduction to the math of neural networks, Heaton Research Inc. (Chesterfield, MO), These have special analysis methods. In particular linear regression techniques are much more efficient than most non-linear techniques. The model can be deterministic or stochastic (i.e.
|
|
In 2006, Polyakov started scientific cooperation with Serge Timashev in the analysis of stochastic time series (Flicker-Noise Spectroscopy). In 2007, he defended the DSc dissertation in Physics and Mathematics at the Karpov Institute of Physical Chemistry, Moscow, Russia.
|
|
An example often considered for adversarial bandits is the iterated prisoner's dilemma. In this example, each adversary has two arms to pull. They can either Deny or Confess. Standard stochastic bandit algorithms don't work very well with this iterations.
|
|
Marc Yor (24 July 1949 – 9 January 2014) was a French mathematician well known for his work on stochastic processes, especially properties of semimartingales, Brownian motion and other Lévy processes, the Bessel processes, and their applications to mathematical finance.
|
|
A stochastic integral, the "Hitsuda-Skorohod integral" can be defined for suitable families \Psi (t) of white noise distributions as a Pettis integral : \int \partial_t^\ast \Psi (t) \, dt\in (S)^\ast, generalizing the Itô integral beyond adapted integrands.
|
|
M. Burkhardt and A. Raghunathan, Proc. SPIE 9422, 94220X (2015). EUV also has issues with reliably printing all features in a large population; some contacts may be completely missing or lines bridged. These are known as stochastic printing failures.
|
|
November 2003. M. J. Neely, E. Modiano, and C. Li, "Fairness and Optimal Stochastic Control for Heterogeneous Networks," Proc. IEEE INFOCOM, March 2005. A. Stolyar, "Maximizing Queueing Network Utility subject to Stability: Greedy Primal-Dual Algorithm," Queueing Systems, vol.
|
|
There is also a compressed MPSC file format. SMPS is a specialized extension, designed to represent stochastic programming problem instances, in use especially in research environments. Although some extensions are not standardized, the format is still in general use.
|
|
Paul-André Meyer (21 August 1934 – 30 January 2003) was a French mathematician, who played a major role in the development of the general theory of stochastic processes. He worked at the Institut de Recherche Mathématique (IRMA) in Strasbourg.
|
|
Due to the equivalence : { (close_{today} - low_{Ndays}) - (close_{today} - high_{Ndays}) = high_{Ndays} - low_{Ndays} } the %R indicator is arithmetically exactly equivalent to the %K stochastic oscillator, mirrored at the 0%-line, when using the same time interval.
|
|
Elefteriadou, An introduction to traffic flow theory. Springer optimization and its applications, vol 84. Springer, Berlin, 2014. The paradigm of standard traffic and transportation theories is that at any time instant there is a value of stochastic highway capacity.
|
|
Typical choices for the grains include disks, random polygon and segments of random length. Boolean models are also examples of stochastic processes known as coverage processes. The above models can be extended from the plane to general Euclidean space .
|
|
Forecast information is essential for an efficient use, the management of the electricity grid and for solar energy trading. Common solar forecasting method include stochastic learning methods, local and remote sensing methods, and hybrid methods (Chu et al. 2016).
|
|
His laboratory has demonstrated the molecular mechanisms that pattern the fly color-sensing photoreceptor neurons and showed how stochastic decisions,Losick R. & Desplan C. Stochastic choices and cell fate, Science 320, 65-68 (2008)Johnston R.J.Jr. & Desplan C. Interchromosomal communication coordinates intrinsically stochastic expression between alleles. Science 343:661-5 (2014) a transcription factor network,Johnston R. Jr. Otake Y., Sood P., Vogt N., Behnia R., Vasiliauskas.D, McDonald E., Xie B., Koenig ., Wolf R., Cook T., Gebelein B., Kussell E., Nagakoshi H. & Desplan C. Interlocked feedforward loops control specific Rhodopsin expression in the Drosophila eye. Cell 145, 956-968 (2011) and a tumor suppressor pathwayMikeladze-Dvali T., Wernet M., Pistillo D. , Mazzoni E. O., Teleman A., Chen Y., Cohen S. & Desplan C. The growth regulators Warts/lats and Melted interact in a bistable loop to specify opposite fates in R8 photoreceptors. Cell, 122, 775-787 (2005).
|
|
Stochastic resonance was first discovered in a study of the periodic recurrence of Earth's ice ages. The theory developed out of an effort to understand how the earth's climate oscillates periodically between two relatively stable global temperature states, one "normal" and the other an "ice age" state. The conventional explanation was that variations in the eccentricity of earth's orbital path occurred with a period of about 100,000 years and caused the average temperature to shift dramatically. The measured variation in the eccentricity had a relatively small amplitude compared to the dramatic temperature change, however, and stochastic resonance was developed to show that the temperature change due to the weak eccentricity oscillation and added stochastic variation due to the unpredictable energy output of the sun (known as the solar constant) could cause the temperature to move in a nonlinear fashion between two stable dynamic states.
|
|
Owen Chamberlain, discoverer of the 'antiproton' and a Berkeley Nobel laureate, to engage in antiproton beam research. He subsequently completed his PhD dissertation on the timely and critical topic of stochastic cooling of bunched beams of antiproton from the University of California (Berkeley) Physics department in 1982 and continued onto CERN as an "attaché scientifique" in the Super Proton Antiproton Synchrotron working with Daniel Boussard, Simon van der Meer and Carlo Rubbia, contributing to the ongoing program of stochastic cooling of antiproton beams, which led to the discovery of the W and Z vector bosons at CERN, and to the early ideas of stochastic cooling of "bunched" beams, which today are being applied successfully to phase space cooling of heavy ions at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory, leading to exciting new investigations of the 'quark-gluon' plasma in gold-on-gold collisions.
|
|
Andrei Andreyevich Markov, Russian mathematician known for his work on Stochastic processes Borkar's researches were mainly in the fields of Stochastic control, Learning control theory and random processes and he is known to have introduced a new convex analytical paradigm based upon occupation measures. His work is reported to have assisted in bettering the understanding of Stochastic control issues and elucidated adaptive control schemes with regard to asymptotic optimality. He has worked on Distributed computation, Multiple timescales, Approximation and learning algorithms, Multiagent problems and Small noise limits and developed a protocol which used conditional version of importance sampling for the estimation of Markov chain averages; the scheme was later confirmed by a team of scientists from Massachusetts Institute of Technology. His researches have been documented in several peer-reviewed articles; and Google Scholar, an online article repository of scientific articles has listed 373 of them.
|
|
There are also alternatives to the static data masking that rely on stochastic perturbations of the data that preserve some of the statistical properties of the original data. Examples of statistical data obfuscation methods include differential privacy and the DataSifter method .
|
|
Panorska's research interests include studying extreme events in the stochastic processes used to model weather, water, and biology. She has also studied the effects of weather conditions on baseball performance, concluding that temperature has a larger effect than wind and humidity.
|
|
Besides, unlike regular lattices, the sizes of its cells are not equal; rather, the distribution of the area size of its blocks obeys dynamic scaling, whose coordination number distribution follows a power-law. A snapshot of the weighted stochastic lattice.
|
|
Leo Breiman. Probability. Original edition published by Addison-Wesley, 1968; reprinted by Society for Industrial and Applied Mathematics, 1992. (See Sections 3.9, 12.9, and 12.10; Theorem 3.52 specifically.)Varadhan, S. R. S. Stochastic Processes. Courant Lecture Notes in Mathematics, 16.
|
|
The homogeneous Poisson process on the real line is considered one of the simplest stochastic processes for counting random numbers of points.D. Snyder and M. Miller. Random point processes in time and space 2e springer-verlag. New York, NY, 1991.
|
|
This algorithm was developed in Dobramysl, U., & Holcman, D. (2018). Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows. Journal of computational physics, 355, 22-36. Dobramysl, U., & Holcman, D. (2019).
|
|
Gérard Ben Arous (born 26 June 1957) is a French mathematician, specializing in stochastic analysis and its applications to mathematical physics. He served as the director of the Courant Institute of Mathematical Sciences at New York University from 2011 to 2016.
|
|
The defect generation in the dielectric is a stochastic process. There are two modes of breakdown, intrinsic and extrinsic. Intrinsic breakdown is caused by electrical stress induced defect generation. Extrinsic breakdown is caused by defects induced by the manufacturing process.
|
|
Wessels was president of the Vereniging voor Statistiek (VVS), and has contributed to the foundation of the National Network Mathematical Decision Making (LNMB), the research school BETA, and European Institute for Statistics, Probability, Stochastic Operations Research and its Applications (EURANDOM).
|
|
Urgaonkar, B. Urgaonkar, M. J. Neely, A. Sivasubramaniam, "Optimal Power Cost Management Using Stored Energy in Data Centers," Proc. SIGMETRICS 2011.M. Baghaie, S. Moeller, B. Krishnamachari, "Energy Routing on the Future Grid: A Stochastic Network Optimization Approach," Proc. International Conf.
|
|
The expectations of general functionals of simple point processes, provided some certain mathematical conditions, have (possibly infinite) expansions or series consisting of the corresponding factorial moment measures.B. Blaszczyszyn. Factorial-moment expansion for stochastic systems. Stoch. Proc. Appl., 56:321–335, 1995.
|
|
Figure 1: CELP decoder Before exploring the complex encoding process of CELP we introduce the decoder here. Figure 1 describes a generic CELP decoder. The excitation is produced by summing the contributions from fixed (a.k.a. stochastic or innovation) and adaptive (a.k.a.
|
|
Perhaps the most common situation in which these are encountered is as the solution to Stratonovich stochastic differential equations (SDEs). These are equivalent to Itô SDEs and it is possible to convert between the two whenever one definition is more convenient.
|
|
The FASTER algorithm uses a combination of deterministic and stochastic criteria to optimize amino acid sequences. FASTER first uses DEE to eliminate rotamers that are not part of the optimal solution. Then, a series of iterative steps optimize the rotamer assignment.
|
|
The σ-algebra of τ-past, (also named stopped σ-algebra, stopped σ-field, or σ-field of τ-past) is a σ-algebra associated with a stopping time in the theory of stochastic processes, a branch of probability theory.
|
|
Alper Demir is a Professor of Electrical Engineering at Koç University in Istanbul, Turkey. He was named a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2012 for his contributions to stochastic modeling and analysis of phase noise.
|
|
For 73:27 the Theil index and the Hoover index are identical: Both are 0.46. For 62:38 the difference between the Theil index (representing stochastic distribution) and the Hoover index (representing a perfectly planned distribution) reaches a minimum of -0.12.
|
|
The process of electron penetration through a resist is essentially a stochastic process; there is a finite probability that resist exposure by released electrons can occur quite far from the point of photon absorption.J. Torok et al., J. Photopolymer Sci.
|
|
Dendropsophus stingi live in flooded pastures, marshes, and temporary pools at about above sea level. No major threats to this species have been identified. It is locally common but its known range is small, making it vulnerable to stochastic events.
|
|
In mathematics, an integration by parts operator is a linear operator used to formulate integration by parts formulae; the most interesting examples of integration by parts operators occur in infinite-dimensional settings and find uses in stochastic analysis and its applications.
|
|
Mixed Poisson processes are doubly stochastic in the sense that in a first step, the value of the random variable X is determined. This value then determines the "second order stochasticity" by increasing or decreasing the original intensity measure \mu .
|
|
The species' natural habitat are cloud forests at elevations of above sea level. It is a terrestrial species found on rocks, or more rarely, in bromeliads. It is a common species but with small range, making it susceptible stochastic threats.
|
|
Several attempts on mathematical modeling and computer simulation of mitotic chromosome assembly, based on molecular activities of condensins, have been reported. Representative ones include modeling based on loop extrusion, stochastic pairwise contacts and a combination of looping and inter-condensin attractions.
|
|
USA 69, 2509-2512. and human sperm chemotaxis,Armon, L. and Eisenbach, M. (2011) Behavioral mechanism during human sperm chemotaxis: Involvement of hyperactivation. PLoS ONE 6, e28359. the behavioral mechanism of human sperm thermotaxis appears to be stochastic rather than deterministic.
|
|
Actuarial loss reserving methods including the chain-ladder method, Bornhuetter-Ferguson method, expected claims technique, and others are used to estimate IBNR and, hence, ultimate losses. Since the implementation of Solvency II, stochastic claims reserving methods have become more common.
|
|
In harmonic analysis, he studied the ergodicity and mixing properties of stationary stochastic processes in terms of their spectral properties. Maruyama also studied quasi-invariance properties of the Wiener measure, extending previous work by Cameron and Martin to diffusion processes.
|
|
In probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely related to the autocorrelation of the process in question.
|
|
In mathematics, Itô's lemma is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule. It can be heuristically derived by forming the Taylor series expansion of the function up to its second derivatives and retaining terms up to first order in the time increment and second order in the Wiener process increment. The lemma is widely employed in mathematical finance, and its best known application is in the derivation of the Black–Scholes equation for option values.
|
|
In 1984, Roald Sagdeev invited Zaslavsky to the Institute of Space Research in Moscow. There he has worked on the theory of degenerate and almost degenerate Hamiltonian systems, anomalous chaotic transport, plasma physics, and theory of chaos in waveguides. The book Nonlinear Physics: from the Pendulum to Turbulence and Chaos (Nauka, Moscow and Harwood, New York, 1988), written with Sagdeev, is now a classical textbook for chaos theory. When studying interaction of a charged particle with a wave packet, Zaslavsky with colleagues from that institute discovered that stochastic layers of different separatrices in degenerated Hamiltonian systems may merge producing a stochastic web.
|
|
QTT has become particularly popular since the technology has become available to efficiently control and monitor individual quantum systems as it can predict how individual quantum objects such as particles will behave when they are observed. In QTT open quantum systems are modelled as scattering processes, with classical external fields corresponding to the inputs and classical stochastic processes corresponding to the outputs (the fields after the measurement process). The mapping from inputs to outputs is provided by a quantum stochastic process that is set up to account for a particular measurement strategy (eg., photon counting, homodyne/heterodyne detection, etc).
|
|
The MLRP is used to represent a data-generating process that enjoys a straightforward relationship between the magnitude of some observed variable and the distribution it draws from. If f(x) satisfies the MLRP with respect to g(x), the higher the observed value x, the more likely it was drawn from distribution f rather than g. As usual for monotonic relationships, the likelihood ratio's monotonicity comes in handy in statistics, particularly when using maximum-likelihood estimation. Also, distribution families with MLR have a number of well-behaved stochastic properties, such as first-order stochastic dominance and increasing hazard ratios.
|
|
He got his B.Sc. (1954) and Ph.D. (1961) at University of London, on the dissertation Stochastic Process in Banach space and its Applications to Congestion Theory. Encouraged by Thomas L. Saaty he moved to College Park, Maryland, joining the mathematics faculty of University of Maryland (1961–1999), founded the journal Stochastic Processes and their Applications (1973) and was fellow of the Institute of Mathematical Statistics. Syski wrote over forty journal articles, often collaborating with notables such as Félix Pollaczek, Lajos Takács, Julian Keilson and Wim Cohen. Syski died of complications from a brain injury received during a fall.
|
|
Many improvements on the basic stochastic gradient descent algorithm have been proposed and used. In particular, in machine learning, the need to set a learning rate (step size) has been recognized as problematic. Setting this parameter too high can cause the algorithm to diverge; setting it too low makes it slow to converge. A conceptually simple extension of stochastic gradient descent makes the learning rate a decreasing function of the iteration number , giving a learning rate schedule, so that the first iterations cause large changes in the parameters, while the later ones do only fine-tuning.
|
|
A stochastic analogue of the standard (deterministic) Newton–Raphson algorithm (a "second-order" method) provides an asymptotically optimal or near-optimal form of iterative optimization in the setting of stochastic approximation. A method that uses direct measurements of the Hessian matrices of the summands in the empirical risk function was developed by Byrd, Hansen, Nocedal, and Singer. However, directly determining the required Hessian matrices for optimization may not be possible in practice. Practical and theoretically sound methods for second-order versions of SGD that do not require direct Hessian information are given by Spall and others.
|
|
Gordon was educated at University of Chicago where he did an undergraduate degree in Mathematics and a PhD at University of Oregon in Chemical Physics under Terrell L Hill. His thesis was On Stochastic Growth and Form and Steady State Properties of Ising Lattice Membranes. He published his first paper in 1966.Gordon, R.On stochastic growth and form Proceedings of the National Academy of Sciences of the United States of America 56(5), 1497-1504 1966 Gordon is an eclectic scientist and prolific writer with over 200 peer reviewed publications in a wide number of fields.
|
|
Various predictive models have been developed for load forecasting based on various techniques like multiple regression, exponential smoothing, iterative reweighted least-squares, adaptive load forecasting, stochastic time series, fuzzy logic, neural networks and knowledge based expert systems. Amongst these, the most popular STLF were stochastic time series models like Autoregressive (AR) model, Autoregressive moving average model (ARMA), Autoregressive integrated moving average (ARIMA) model and other models using fuzzy logic and Neural Networks. DLF provides data aggregation and forecasting capabilities that is configured to address today’s requirements and adapt to address future requirements and should have the capability to produce repeatable and accurate forecasts.
|
|
Inventory optimization models can be either deterministic—with every set of variable states uniquely determined by the parameters in the model – or stochastic—with variable states described by probability distributions.Leslie Hansen Harps, “Optimizing Your Supply Chain: A Model Approach,” Inbound Logistics, April 2003. Stochastic optimization takes supply uncertainty into account that, for example, 6 percent of orders from an overseas supplier are 1–3 days late, 1 percent are 4–6 days late, 5 percent are 7–14 days late and 8 percent are more than 14 days late.“Are Your Inventory Management Practices Outdated,” AberdeenGroup, March 1, 2005.
|
|
The scheme could then be used to "cool" (to collimate) the anti- protons, which could thus be forced into a well-focused beam, suitable for acceleration to high energies, without losing too many anti-protons to collisions with the structure. Stochastic expresses the fact that signals to be taken resemble random noise, which was called "Schottky noise" when first encountered in vacuum tubes. Without van der Meer's technique, UA1 would never have had the sufficient high-intensity anti-protons it needed. Without Rubbia's realisation of its usefulness, stochastic cooling would have been the subject of a few publications and nothing else.
|
|
Evans in 2014 Steven Neil Evans (born 12 August 1960) is an Australian- American statistician and mathematician, specializing in stochastic processes.Steven N. Evans homepage at U.C. Berkeley (with links to online publications) Evans was born, Orange, New South Wales. In 1982 he obtained his bachelor's degree from the University of Sydney and in 1987 his Ph.D. from the University of Cambridge under Martin T. Barlow with thesis Local Properties of Markov Families and Stochastic Processes Indexed by a Totally Disconnected Field. From 1987 to 1991 he was an assistant professor of statistics at the University of California, Berkeley.
|
|
SED describes energy contained in the electromagnetic vacuum at absolute zero as a stochastic, fluctuating zero- point field. The motion of a particle immersed in this stochastic zero-point radiation generally results in highly nonlinear, sometimes chaotic or emergent, behaviour. Modern approaches to SED consider the quantum properties of waves and particles as well-coordinated emergent effects resulting from deeper (sub-quantum) nonlinear matter-field interactions. Given the posited emergent nature of quantum laws in SED, it has been argued that they form a kind of "quantum equilibrium" that has an analogous status to that of thermal equilibrium in classical dynamics.
|
|
SED describes electromagnetic energy at absolute zero as a stochastic, fluctuating zero-point field. In SED the motion of a particle immersed in the stochastic zero-point radiation field generally results in highly nonlinear behaviour. Quantum effects emerge as a result of permanent matter-field interactions not possible to describe in QED The typical mathematical models used in classical electromagnetism, quantum electrodynamics (QED) and the standard model view electromagnetism as a U(1) gauge theory, which topologically restricts any complex nonlinear interaction. The electromagnetic vacuum in these theories is generally viewed as a linear system with no overall observable consequence.
|
|
McDonnell graduated from the Salesian College, Adelaide.McDonnell's high school He received a BSc in Mathematical & Computer Sciences (1997), a BE (Hons) in Electrical & Electronic Engineering (1998), and a BSc (Hons) in Applied Mathematics (2001) all from The University of Adelaide, Australia. He received his PhD in Electrical & Electronic Engineering (2006), under Derek Abbott and Charles E. M. Pearce, also from the University of Adelaide, for a thesis entitled Theoretical Aspects of Stochastic Signal Quantisation and Suprathreshold Stochastic Resonance. During the course of his PhD, he was also a visiting scholar at the University of Warwick, UK, under Nigel G. Stocks.
|
|
His article on Markov chain models Markov Chain Models in life insurance, Blätter Deutsch. Gesellsch.Versich.math. has been named one of the four most significant papers in modern actuarial science. Hoem also made contributions to stochastic stable population theory,Stochastic stable population theory with continuous time,(with Niels Keiding). Scand. Act. J. 1976 (3), 150-175 (1976) demographic incidence rates,Demographic incidence rates. Theor. Popul. Biol. 14 (3), 329-337. Bibliographic Note, 18 (2), 195 (1978) and the statistical analysis of multiplicative models. He is best known for his work on event-history analysis—contributions that have helped shape demographic methodology.
|
|
Stochastic quantization serves to quantize Euclidean field theories, and is used for numerical applications, such as numerical simulations of gauge theories with fermions. This serves to address the problem of fermion doubling that usually occurs in these numerical calculations. Stochastic quantization takes advantage of the fact that a Euclidean quantum field theory can be modeled as the equilibrium limit of a statistical mechanical system coupled to a heat bath. In particular, in the path integral representation of a Euclidean quantum field theory, the path integral measure is closely related to the Boltzmann distribution of a statistical mechanical system in equilibrium.
|
|
Wold's thesis, A Study in the analysis of stationary time series, was an important contribution. The main result was the "Wold decomposition" by which a stationary series is expressed as a sum of a deterministic component and a stochastic component which can itself be expressed as an infinite moving average. Beyond this, the work brought together for the first time the work on individual processes by English statisticians, principally Udny Yule, and the theory of stationary stochastic processes created by Russian mathematicians, principally A. Ya. Khinchin. Wold's results on univariate time series were generalized to multivariate time series by his student Peter Whittle.
|
|
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process (or deterministic system). Instead of dealing with only one possible reality of how the process might evolve over time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths may be more probable and others less so.
|
|
Stochastic resonance has been observed in the neural tissue of the sensory systems of several organisms. Computationally, neurons exhibit SR because of non-linearities in their processing. SR has yet to be fully explained in biological systems, but neural synchrony in the brain (specifically in the gamma wave frequency) has been suggested as a possible neural mechanism for SR by researchers who have investigated the perception of "subconscious" visual sensation. Single neurons in vitro including cerebellar Purkinje cells and squid giant axon could also demonstrate the inverse stochastic resonance, when spiking is inhibited by synaptic noise of a particular variance.
|
|
Van Schuppen's research interest are in the areas of systems theory and probability. These include system identification, and realization theory, and the area of control theory, with control of discrete-event systems, control of hybrid systems, control and system theory of positive systems, control of stochastic systems, and adaptive control. He worked also on the filtering problem, on dynamic games and team problems, on probability and stochastic processes, and on applications of the theory including control and system theory of biochemical reaction networks, control of communication systems and networks, and control of motorway traffic in a consultancy for the Dutch administration.
|
|
Stochastic resonance was demonstrated in a high-level mathematical model of a single neuron using a dynamical systems approach. The model neuron was composed of a bi-stable potential energy function treated as a dynamical system that was set up to fire spikes in response to a pure tonal input with broadband noise and the SNR is calculated from the power spectrum of the potential energy function, which loosely corresponds to an actual neuron's spike-rate output. The characteristic peak on a plot of the SNR as a function of noise variance was apparent, demonstrating the occurrence of stochastic resonance.
|
|
Deep learning training mainly relies on variants of stochastic gradient descent, where gradients are computed on a random subset of the total dataset and then used to make one step of the gradient descent. Federated stochastic gradient descentPrivacy Preserving Deep Learning, R. Shokri and V. Shmatikov, 2015 is the direct transposition of this algorithm to the federated setting, but by using a random fraction C of the nodes and using all the data on this node. The gradients are averaged by the server proportionally to the number of training samples on each node, and used to make a gradient descent step.
|
|
When such volatility has a randomness of its own—often described by a different equation driven by a different W—the model above is called a stochastic volatility model. And when such volatility is merely a function of the current asset level St and of time t, we have a local volatility model. The local volatility model is a useful simplification of the stochastic volatility model. "Local volatility" is thus a term used in quantitative finance to denote the set of diffusion coefficients, \sigma_t = \sigma(S_t,t), that are consistent with market prices for all options on a given underlying.
|
|
The set T is called the index set or parameter set of the stochastic process. Often this set is some subset of the real line, such as the natural numbers or an interval, giving the set T the interpretation of time. In addition to these sets, the index set T can be other linearly ordered sets or more general mathematical sets, such as the Cartesian plane R^2 or n-dimensional Euclidean space, where an element t\in T can represent a point in space. But in general more results and theorems are possible for stochastic processes when the index set is ordered.
|
|
To represent stochastic risk the dose quantities equivalent dose H T and effective dose E are used, and appropriate dose factors and coefficients are used to calculate these from the absorbed dose. Equivalent and effective dose quantities are expressed in units of the sievert or rem which implies that biological effects have been taken into account. The derivation of stochastic risk is in accordance with the recommendations of the International Committee on Radiation Protection (ICRP) and International Commission on Radiation Units and Measurements (ICRU). The coherent system of radiological protection quantities developed by them is shown in the accompanying diagram.
|
|
Then, the significant contributors such as S. Kusuoka, D. Stroock, Bismut, S. Watanabe, I. Shigekawa, and so on finally completed the foundations. Malliavin calculus is named after Paul Malliavin whose ideas led to a proof that Hörmander's condition implies the existence and smoothness of a density for the solution of a stochastic differential equation; Hörmander's original proof was based on the theory of partial differential equations. The calculus has been applied to stochastic partial differential equations as well. The calculus allows integration by parts with random variables; this operation is used in mathematical finance to compute the sensitivities of financial derivatives.
|
|
In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. The moving-average model specifies that the output variable depends linearly on the current and various past values of a stochastic (imperfectly predictable) term. Together with the autoregressive (AR) model, the moving- average model is a special case and key component of the more general ARMA and ARIMA models of time series, which have a more complicated stochastic structure. The moving-average model should not be confused with the moving average, a distinct concept despite some similarities.
|
|
The memory-based Yule-Simon (MBYS) model attempts to explain tag choices by a stochastic process. It was found that the temporal order of tag assignment influences users' tag choices. Similar to the stochastic urn model, the MBYS model assumes that at each step, a tag would be randomly sampled: with probability p that the sampled tag was new, and with probability 1-p that the sampled tag was copied from existing tags. When copying, the probability of selecting a tag was assumed to decay with time, and this decay function was found to follow a power-law distribution.
|
|
With extensive financial support from the National Science Foundation, their work on the stochastic framework led to the creation of the web-based system ALEKS for the assessment and learning of mathematics and science. Falmagne and Doignon's 2011 book, Learning Spaces, contains the most current presentation and development of the stochastic framework for the assessment of knowledge. Learning spaces are specific kinds of knowledge spaces, whose best applications are to situations where assessments guide efficient learning. Learning spaces are a part of the concept of Media Theory, which explores the modeling of knowledge structures and knowledge states.
|
|
Pascal Van Hentenryck (born 8 March 1963) is the A. Russell Chandler III Chair and Professor of Industrial and Systems Engineering at Georgia Tech. He is credited with pioneering advances in constraint programming and stochastic optimization, bridging theory and practice to solve real-world problems across a range of domains including sports scheduling, protein folding, kidney matching, disaster relief, power systems, recommender systems, and transportation. He has developed several optimization technologies including CHIP, Numerica, the Optimization Programming Language (OPL - now an IBM product), and Comet. He has also published several books, including Online Stochastic Combinatorial Optimization, Hybrid Optimization, and Constraint- Based Local Search.
|
|
Technically speaking, Phillips (1986) proved that parameter estimates will not converge in probability, the intercept will diverge and the slope will have a non-degenerate distribution as the sample size increases. However, there might be a common stochastic trend to both series that a researcher is genuinely interested in because it reflects a long-run relationship between these variables. Because of the stochastic nature of the trend it is not possible to break up integrated series into a deterministic (predictable) trend and a stationary series containing deviations from trend. Even in deterministically detrended random walks spurious correlations will eventually emerge.
|
|
In the former case of a unit root, stochastic shocks have permanent effects, and the process is not mean- reverting. In the latter case of a deterministic trend, the process is called a trend-stationary process, and stochastic shocks have only transitory effects after which the variable tends toward a deterministically evolving (non- constant) mean. A trend stationary process is not strictly stationary, but can easily be transformed into a stationary process by removing the underlying trend, which is solely a function of time. Similarly, processes with one or more unit roots can be made stationary through differencing.
|
|
D. Banabic et al "Sheet Metal Forming Processes, Constitutive Modelling and Numerical Simulation", 2010, pages 218-230. In addition to the use of incremental solver technology, the Solution for Production also applies stochastic methods to model the potential for variations in the inputs commonly associated with Sheet Metal Forming Simulation in doing so users can predict the potential for robustness of the sheet metal forming process during the design evaluation and validation. By modeling the effect of production noise Cp and Cpk (process capability index) in production can be predicted. Another use of the stochastic model is to vary design variables.
|
|
The new paradigm of traffic and transportation science following from the empirical nucleation nature of traffic breakdown (F → S transition) and Kerner's three-phase traffic theory changes fundamentally the meaning of stochastic highway capacity as follows. At any time instant there is a range of highway capacity values between a minimum and a maximum highway capacity, which are themselves stochastic values. When the flow rate at a bottleneck is inside this capacity range related to this time instant, traffic breakdown can occur at the bottleneck only with some probability, i.e., in some cases traffic breakdown occurs, in other cases it does not occur.
|
|
The committed dose in radiological protection is a measure of the stochastic health risk due to an intake of radioactive material into the human body. Stochastic in this context is defined as the probability of cancer induction and genetic damage, due to low levels of radiation. The SI unit of measure is the sievert. A committed dose from an internal source represents the same effective risk as the same amount of effective dose applied uniformly to the whole body from an external source, or the same amount of equivalent dose applied to part of the body.
|
|
In probability and statistics, point process notation comprises the range of mathematical notation used to symbolically represent random objects known as point processes, which are used in related fields such as stochastic geometry, spatial statistics and continuum percolation theory and frequently serve as mathematical models of random phenomena, representable as points, in time, space or both. The notation varies due to the histories of certain mathematical fields and the different interpretations of point processes,D. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. Stochastic geometry and its applications, Second Edition, Section 4.1, Wiley Chichester, 1995.
|
|
Zakai's main research concentrated on the study of the theory of stochastic processes and its application to information and control problems; namely, problems of noise in communication radar and control systems. The basic class of random processes which represent the noise in such systems are known as "white noise" or the "Wiener process" where the white noise is "something like a derivative" of the Wiener process. Since these processes vary quickly with time, the classical differential and integral calculus is not applicable to such processes. In the 1940s Kiyoshi Itō developed a stochastic calculus (the Ito calculus) for such random processes.
|
|
In addition to the Ito calculus, Paul Malliavin developed in the 1970s a "stochastic calculus of variations" known as the "Malliavin calculus". It turned out that in this setup it is possible to define a stochastic integral which will include the Ito integral. The papers of Zakai with David Nualart, Ali Süleyman Üstünel and Zeitouni promoted the understanding and applicability of the Malliavin calculus. The monograph of Üstünel and Zakai deals with the application of the Malliavin calculus to derive relations between the Wiener process and other processes which are in some sense "similar" to the probability law of the Wiener process.
|
|
The French mathematician Paul Lévy proved the following theorem, which gives a necessary and sufficient condition for a continuous Rn- valued stochastic process X to actually be n-dimensional Brownian motion. Hence, Lévy's condition can actually be used as an alternative definition of Brownian motion. Let X = (X1, ..., Xn) be a continuous stochastic process on a probability space (Ω, Σ, P) taking values in Rn. Then the following are equivalent: # X is a Brownian motion with respect to P, i.e., the law of X with respect to P is the same as the law of an n-dimensional Brownian motion, i.e.
|
|
Harold Joseph Kushner is an American applied mathematician and a Professor Emeritus of Applied Mathematics at Brown University. He is known for his work on the theory of stochastic stability (based on the concept of supermartingales as Lyapunov functions), the theory of non-linear filtering (based on the Kushner equation), and for the development of numerical methods for stochastic control problems such as the Markov chain approximation method. He is commonly cited as the first person to study Bayesian optimization, based on work he published in 1964. Harold Kushner received his Ph.D. in Electrical Engineering from the University of Wisconsin in 1958.
|
|
For example, the difference in approach between MDPs and the minimax solution is that the latter considers the worst-case over a set of adversarial moves, rather than reasoning in expectation about these moves given a fixed probability distribution. The minimax approach may be advantageous where stochastic models of uncertainty are not available, but may also be overestimating extremely unlikely (but costly) events, dramatically swaying the strategy in such scenarios if it is assumed that an adversary can force such an event to happen. (See Black swan theory for more discussion on this kind of modeling issue, particularly as it relates to predicting and limiting losses in investment banking.) General models that include all elements of stochastic outcomes, adversaries, and partial or noisy observability (of moves by other players) have also been studied. The "gold standard" is considered to be partially observable stochastic game (POSG), but few realistic problems are computationally feasible in POSG representation.
|
|
In his work a simple example of an anharmonic oscillator driven by a superposition of incoherent sinusoidal oscillations with continuous spectrum was used to show that depending on a specific approximation time scale the evolution of the system can be either deterministic, or a stochastic process satisfying Fokker–Planck equation, or even a process which is neither deterministic nor stochastic. In other words, he showed that depending on the choice of the time scale for the corresponding approximations the same stochastic process can be regarded as both dynamical and Markovian, and in the general case as a non-Markov process. This work was the first to introduce the notion of time hierarchy in non-equilibrium statistical physics which then became the key concept in all further development of the statistical theory of irreversible processes. In 1945, Bogolyubov proved a fundamental theorem on the existence and basic properties of a one-parameter integral manifold for a system of non-linear differential equations.
|
|
The Calogero conjecture is a minority interpretation of quantum mechanics. It is a quantization explanation involving quantum mechanics, originally stipulated in 1997 and further republished in 2004 by Francesco Calogero that suggests the classical stochastic background field to which Edward Nelson attributes quantum mechanical behavior in his theory of stochastic quantization is a fluctuating space-time, and that there are further mathematical relations between the involved quantities. The hypothesis itself suggests that if the angular momentum associated with a stochastic tremor with spatial coherence provides an action purported by that motion within the order of magnitude of Planck's constant then the order of magnitude of the associated angular momentum has the same value. Calogero himself suggests that these findings, originally based on the simplified model of the universe "are affected (and essentially, unaffected) by the possible presence in the mass of the Universe of a large component made up of particles much lighter than nucleons".
|
|
Asymptotic Problems in Stochastic Processes and PDE's, retrieved 2015-01-19. In 2012, he became one of the inaugural fellows of the American Mathematical Society.List of Fellows of the American Mathematical Society, retrieved 2015-01-19. His doctoral students include Jürgen Gärtner.
|
|
Wonham attended a boys’ school and preferred individual to team sports, taking up sailing and tennis. Wonham obtained his bachelor's degree in engineering physics from McGill University in 1956, and then a doctorate in stochastic control from the University of Cambridge in 1961.
|
|
CRC Press, 2003. which are applied in various scientific and engineering disciplines such as biology, geology, physics, and telecommunications.F. Baccelli and B. Błaszczyszyn. Stochastic Geometry and Wireless Networks, Volume I – Theory, volume 3, No 3-4 of Foundations and Trends in Networking.
|
|
A real-valued stochastic process is a submartingale if and only if it has a Doob decomposition into a martingale and an integrable predictable process that is almost surely increasing. It is a supermartingale, if and only if is almost surely decreasing.
|
|
Kurt Wiesenfeld is an American physicist working primarily on non-linear dynamics. His works primarily concern stochastic resonance, spontaneous synchronization of coupled oscillators, and non-linear laser dynamics. Since 1987, he has been professor of physics at the Georgia Institute of Technology.
|
|
This idea is seen again when one considers percentiles (see percentile). When assessing risks at specific percentiles, the factors that contribute to these levels are rarely at these percentiles themselves. Stochastic models can be simulated to assess the percentiles of the aggregated distributions.
|
|
Estimating future claims liabilities might also involve estimating the uncertainty around the estimates of claim reserves. See J Li's article "Comparison of Stochastic Reserving Models" (published in the Australian Actuarial Journal, volume 12 issue 4) for a recent article on this topic.
|
|
D. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. Stochastic geometry and its applications, volume 2. Wiley Chichester, 1995. Factorial moment measures completely characterize a wide class of point processes, which means they can be used to uniquely identify a point process.
|
|
Carlo Jaeger and Prof. Klaus Hasselmann. Hasselmann has published papers on climate dynamics, stochastic processes, ocean waves, remote sensing, and integrated assessment studies. His reputation in oceanography was primarily founded on a set of papers on non-linear interactions in ocean waves.
|
|
Rachel Ward and Deanna Needell received the IMA Prize in Mathematics and Applications in 2016. The award recognized their theoretical work related to medical sensing and MRIs, with Needell recognized in particular for her contributions to sparse approximation, signal processing, and stochastic optimization.
|
|
Hansen–Jagannathan bound is a theorem in financial economics that says that the ratio of the standard deviation of a stochastic discount factor to its mean exceeds the Sharpe ratio attained by any portfolio. This result applies, among others, the Cauchy–Schwarz inequality.
|
|
Stochastics and Dynamics (SD) is an interdisciplinary journal published by World Scientific. It was founded in 2001 and covers "modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system's point of view".World Scientific. Journal Aims & Scope.
|
|
Abstract Thesis (PhD in Engineering Science)--Univ. of California, Jan. 1965. Bibliography: l. 81-88. Publisher [Berkeley] Repository OCLC's Experimental Thesis Catalog (United States) In 1965 Wets befriended R. Tyrrell Rockafellar, whom Wets introduced to stochastic optimization, starting a collaboration of many decades.
|
|
Null Device has also contributed to various projects with a number of other industrial, synthpop and electronic artists, including Armageddon Dildos, B! Machine, Blind Faith and Envy, Caustic, The Dark Clan, Distorted Reality, The Gothsicles, Epsilon Minus, Hungry Lucy, Stochastic Theory and Stromkern.
|
|
The gravitational wave background (also GWB and stochastic background) is a random gravitational-wave signal potentially detectable by gravitational wave detection experiments. Since the background is supposed to be random it is completely determined by its statistical properties such as mean, variance etc.
|
|
In statistics, burstiness is the intermittent increases and decreases in activity or frequency of an event.Lambiotte, R. (2013.) "Burstiness and Spreading on Temporal Networks", University of Namur.Neuts, M. F. (1993.) "The Burstiness of Point Processes", Commun. Statist.—Stochastic Models, 9(3):445–66.
|
|
In mathematics, finite-dimensional distributions are a tool in the study of measures and stochastic processes. A lot of information can be gained by studying the "projection" of a measure (or process) onto a finite-dimensional vector space (or finite collection of times).
|
|
A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically modelled as a simple or compound Poisson process.Tankov, P. (2003). Financial modelling with jump processes (Vol. 2). CRC press.
|
|
Developmental noise is a concept within developmental biology in which the phenotype varies between individuals even though both the genotypes and the environmental factors are the same for all of them. Contributing factors include stochastic gene expression and other sources of cellular noise.
|
|
In probability theory, the ladder height process is a record of the largest or smallest value a given stochastic process has achieved up to the specified point in time. The Wiener-Hopf factorization gives the transition probability kernel in the discrete time case.
|
|
The equipment was subsequently transferred to Brookhaven National Laboratory, where it was successfully used in a longitudinal cooling system in RHIC, operationally used beginning in 2006. Since 2012 RHIC has 3D operational stochastic cooling, i.e. cooling the horizontal, vertical, and longitudinal planes.
|
|
In the mathematics of probability, a transition kernel or kernel is a function in mathematics that has different applications. Kernels can for example be used to define random measures or stochastic processes. The most important example of kernels are the Markov kernels.
|
|
The evolution of multiple patterning is being considered in parallel with the emergence of EUV lithography. While EUV lithography satisfies 10-20 nm resolution by basic optical considerations, the occurrence of stochastic defectsP. De Bisschop and E. Hendrickx, Proc. SPIE 10583, 105831K (2018).
|
|
In the study of stochastic processes in mathematics, a hitting time (or first hit time) is the first time at which a given process "hits" a given subset of the state space. Exit times and return times are also examples of hitting times.
|
|
The problem of computing the Birkhoff decomposition with the minimum number of terms has been shown to be NP-hard, but some heuristics for computing it are known. This theorem can be extended for the general stochastic matrix with deterministic transition matrices.
|
|
This zieria is listed as "Endangered" under the Queensland Nature Conservation Act 1992 and under the Commonwealth Government Environment Protection and Biodiversity Conservation Act 1999 (EPBC) Act. The main threat to its survival is stochastic events because of the species' limited distribution.
|
|
A method for testing the behavior of shear thickening fluids is stochastic rotation dynamics-molecular dynamics (SRD-MD). The colloidal particles of a shear thickening fluid are simulated, and shear is applied. These particles create hydroclusters which exert a drag force resisting flow.
|
|
Magda Peligrad is a Romanian mathematician and mathematical statistician known for her research in probability theory, and particularly on central limit theorems and stochastic processes. She works at the University of Cincinnati, where she is Distinguished Charles Phelps Taft Professor of Mathematical Sciences.
|
|
Alladi Ramakrishnan (9 August 1923 – 7 June 2008) was an Indian physicist and the founder of the Institute of Mathematical Sciences (Matscience) in Chennai. He made contributions to stochastic process, particle physics, algebra of matrices, special theory of relativity and quantum mechanics.
|
|
The carcass was soon replaced with suitable density blocks, often gelatin, to ease testing. Current testing is mainly conducted with computer simulation,V. Bheemreddy et al., "Study of Bird Strikes Using Smooth Particle Hydrodynamics and Stochastic Parametric Evaluation," Journal of Aircraft, Vol.
|
|
In probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes, plays the role that the transition matrix does in the theory of Markov processes with a finite state space.
|
|
As such, the software incorporates a number of computational features to facilitate probabilistic simulation of complex systems, including tools for generating and correlating stochastic time series, advanced sampling capabilities (including latin hypercube sampling, nested Monte Carlo analysis, and importance sampling), and support for distributed processing.
|
|
The ECN phenomenon belongs to the general category of random low frequency stochastic processes described by either probability density function equations or in statistical terms. These random processes are either stationary or non-stationary. The first moments of a stationary process are invariate with time.
|
|
MFO, 2008 Stefanie Petermichl (born 1971) is a German mathematical analyst who works as a professor at the University of Toulouse, in France.Short vita, retrieved 2016-07-04. Topics of her research include harmonic analysis, several complex variables, stochastic control, and elliptic partial differential equations.
|
|
Walter Ledermann FRSE (18 March 1911, Berlin, Germany – 22 May 2009, London, England) was a German and British mathematician who worked on matrix theory, group theory, homological algebra, number theory, statistics, and stochastic processes. He was elected to the Royal Society of Edinburgh in 1944.
|
|
Vlachos' approach to modeling is identified by its breadth of scale from molecular, to particle, and macroscale for applications across reaction chemistry, separations, and biology. His interests also include advanced approaches to couple molecular dynamics with quantum mechanical simulations as well as accelerate stochastic simulations.
|
|
We refer to second-order cone programs as deterministic second-order cone programs since data defining them are deterministic. Stochastic second-order cone programs are a class of optimization problems that are defined to handle uncertainty in data defining deterministic second-order cone programs.
|
|
Randomly selects a candidate item and discards it to make space when necessary. This algorithm does not require keeping any information about the access history. For its simplicity, it has been used in ARM processors.ARM Cortex-R series processors manual It admits efficient stochastic simulation.
|
|
In models of this type, numerical methods provide approximate theoretical prices. These are also required in most models that specify the credit risk as a stochastic function with an IR correlation. Practitioners typically use specialised Monte Carlo methods or modified Binomial Tree numerical solutions.
|
|
The damage to the cell can be lethal (the cell dies) or sublethal (the cell can repair itself). Cell damage can ultimately lead to health effects which can be classified as either Tissue Reactions or Stochastic Effects according to the International Commission on Radiological Protection.
|
|
Stochastic effects do not have a threshold of irradiation, are coincidental, and cannot be avoided. They can be divided into somatic and genetic effects. Among the somatic effects, secondary cancer is the most important. It develops because radiation causes DNA mutations directly and indirectly.
|
|
Deterministic inversions address this problem by constraining the answer in some way, usually to well log data. Stochastic inversions address this problem by generating a range of plausible solutions, which can then be narrowed through testing for best fit against various measurements (including production data).
|
|
Warfield's father was mathematician Edward J. McShane.New York Times:Edward McShane, 85, Mathematician, Dies; June 06, 1989 She received her Ph.D. in mathematics from Brown University in 1971. Her doctoral advisor was Wendell Fleming and the title of her dissertation was A Stochastic Minimum Principle.
|
|
The International Journal of Theoretical and Applied Finance was founded in 1998 and is published by World Scientific. It covers the use of quantitative tools in finance, including articles on development and simulation of mathematical models, their industrial usage, and application of modern stochastic methods.
|
|
Sequentially ordered mutations accumulate in driver genes, tumour suppressor genes, and DNA repair enzymes, resulting in clonal expansion of tumour cells. Linear expansion is less likely to reflect the endpoint of a malignant tumour because the accumulation of mutations is stochastic in heterogeneic tumours.
|
|
The concept of the Markov property was originally for stochastic processes in continuous and discrete time, but the property has been adapted for other index sets such as n-dimensional Euclidean space, which results in collections of random variables known as Markov random fields.
|
|
Risk and complexity in scenario optimization. Mathematical Programming, published online, 2019. (see scenario optimization). In 2012 he was elevated to the grade of Fellow of the Institute of Electrical and Electronics Engineers (IEEE) for contributions to stochastic and randomized methods in systems and control.
|
|
Translation as 'The actual content of quantum theoretical kinematics and mechanics' here However, if collapse were a fundamental physical phenomenon, rather than just the epiphenomenon of some other process, it would mean nature was fundamentally stochastic, i.e. nondeterministic, an undesirable property for a theory.
|
|
Stochastic domination is equivalent to saying that \langle f\rangle_1 \ge \langle f\rangle_2 for all increasing ƒ, thus we get a proof of the Holley inequality. (And thus also a proof of the FKG inequality, without using the Harris inequality.) See and for details.
|
|
Numerical Linear Algebra (1st ed.). Philadelphia: SIAM. stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology. Before the advent of modern computers, numerical methods often depended on hand interpolation formulas applied to data from large printed tables.
|
|
Among the list of new applications in mathematics there are new approaches to probability, hydrodynamics,Capinski M., Cutland N. J. Nonstandard Methods for Stochastic Fluid Mechanics. Singapore etc., World Scientific Publishers (1995) measure theory,Cutland N. Loeb Measures in Practice: Recent Advances. Berlin etc.
|
|
In mathematics, the Kolmogorov continuity theorem is a theorem that guarantees that a stochastic process that satisfies certain constraints on the moments of its increments will be continuous (or, more precisely, have a "continuous version"). It is credited to the Soviet mathematician Andrey Nikolaevich Kolmogorov.
|
|
He is also one of the leading theoreticians in the fields of fluid dynamics and theory of turbulence, stochastic processes, phase transitions, laser physics, nuclear physics, transport theory, Bose-E instein condensation and the general statistical physics, as well as mathematical physics and functional analysis.
|
|
In Michigan-style systems, classifiers are contained within a population [P] that has a user defined maximum number of classifiers. Unlike most stochastic search algorithms (e.g. evolutionary algorithms), LCS populations start out empty (i.e. there is no need to randomly initialize a rule population).
|
|
Lenses can focus a beam, reducing its size in one transverse dimension while increasing its angular spread, but cannot change the total emittance. This is a result of Liouville's theorem. Ways of reducing the beam emittance include radiation damping, stochastic cooling, and electron cooling.
|
|
Ruth Jeannette Williams is an Australian-born American mathematician at the University of California, San Diego where she holds the Charles Lee Powell Chair as a Distinguished Professor of Mathematics. Her research concerns probability theory and stochastic processes.Ruth Williams, UCSD, retrieved 2014-12-24.
|
|
This is similar to explicit elastic deformations of the input images, which delivers excellent performance on the MNIST data set. Using stochastic pooling in a multilayer model gives an exponential number of deformations since the selections in higher layers are independent of those below.
|
|
Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD), is a particle-based mesoscale simulation technique for complex fluids which fully incorporates thermal fluctuations and hydrodynamic interactions. Coupling of embedded particles to the coarse-grained solvent is achieved through molecular dynamics.
|
|
SELDM is a stochastic model because it uses Monte Carlo methods to produce the random combinations of input variable values needed to generate the stochastic population of values for each component variable. SELDM calculates the dilution of runoff in the receiving waters and the resulting downstream event mean concentrations and annual average lake concentrations. Results are ranked, and plotting positions are calculated, to indicate the level of risk of adverse effects caused by runoff concentrations, flows, and loads on receiving waters by storm and by year. Unlike deterministic hydrologic models, SELDM is not calibrated by changing values of input variables to match a historical record of values.
|
|
Eigen and colleagues argued that simple package of genes cannot solve the information integration problem and hypercycles cannot be simply replaced by compartments, but compartments may assist hypercycles. This problem, however, raised more objections, and Eörs Szathmáry and László Demeter reconsidered whether packing hypercycles into compartments is a necessary intermediate stage of the evolution. They invented a stochastic corrector model that assumed that replicative templates compete within compartments, and selective values of these compartments depend on the internal composition of templates. Numerical simulations showed that when stochastic effects are taken into account, compartmentalization is sufficient to integrate information dispersed in competitive replicators without the need for hypercycle organization.
|
|
Xiu (in his PhD under Karniadakis at Brown University) generalized the result of Cameron–Martin to various continuous and discrete distributions using orthogonal polynomials from the so-called Askey-scheme and demonstrated L_2 convergence in the corresponding Hilbert functional space. This is popularly known as the generalized polynomial chaos (gPC) framework. The gPC framework has been applied to applications including stochastic fluid dynamics, stochastic finite elements, solid mechanics, nonlinear estimation, the evaluation of finite word-length effects in non-linear fixed-point digital systems and probabilistic robust control. It has been demonstrated that gPC based methods are computationally superior to Monte-Carlo based methods in a number of applications .
|
|
The software is based on the stochastic reactor model (SRM), which is stated in terms of a weighted stochastic particle ensemble. SRM is particular useful in the context of engine modelling as the dynamics of the particle ensemble includes detailed chemical kinetics whilst accounting for inhomogeneity in composition and temperature space arising from on-going fuel injection, heat transfer and turbulence mixing events. Through this coupling, heat release profiles and in particular the associated exhaust gas emissions (Particulates, NOx, Carbon monoxide, Unburned hydrocarbon etc.) can be predicted more accurately than if using the more conventional approaches of standard homogenous and multi-zone reactor methods.
|
|
In continuous time dynamical systems, chaos is the phenomenon of the spontaneous breakdown of topological supersymmetry, which is an intrinsic property of evolution operators of all stochastic and deterministic (partial) differential equations. This picture of dynamical chaos works not only for deterministic models, but also for models with external noise which is an important generalization from the physical point of view, since in reality, all dynamical systems experience influence from their stochastic environments. Within this picture, the long-range dynamical behavior associated with chaotic dynamics (e.g., the butterfly effect) is a consequence of the Goldstone's theorem—in the application to the spontaneous topological supersymmetry breaking.
|
|
Peter Edwin Caines, FRSC is a control theorist and James McGill Professor and Macdonald Chair in Department of Electrical and Computer Engineering at McGill University, Montreal, Quebec, Canada, which he joined in 1980. He is a Fellow of the IEEE, SIAM, the Institute of Mathematics and its Applications, the Canadian Institute for Advanced Research and Royal Society of Canada. He is the recipient of Bode Lecture Prize in 2009 for fundamental contributions in the areas of stochastic, adaptive, large scale and hybrid systems. He initiated the Mean Field Games (or Nash Certainty Equivalence) in engineering with his co-workers for the analysis and control of large population stochastic dynamic systems.
|
|
In estimation theory in statistics, stochastic equicontinuity is a property of estimators (estimation procedures) that is useful in dealing with their asymptotic behaviour as the amount of data increases. It is a version of equicontinuity used in the context of functions of random variables: that is, random functions. The property relates to the rate of convergence of sequences of random variables and requires that this rate is essentially the same within a region of the parameter space being considered. For instance, stochastic equicontinuity, along with other conditions, can be used to show uniform weak convergence, which can be used to prove the convergence of extremum estimators.
|
|
In filtering theory the Zakai equation is a linear stochastic partial differential equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear stochastic partial differential equation for the normalized density of the hidden state. In principle either approach allows one to estimate a quantity function (the state of a dynamical system) from noisy measurements, even when the system is non-linear (thus generalizing the earlier results of Wiener and Kalman for linear systems and solving a central problem in estimation theory). The application of this approach to a specific engineering situation may be problematic however, as these equations are quite complex.
|
|
The school of the NAS academician Yu. M. Berezansky constructed the theory of generalized functions of infinitely many variables on the basis of spectral approach and operators of generalized translation. The school of the NAS academician A. V. Skorokhod investigated a broad range of problems related to random processes and stochastic differential equations. Heuristic methods of phase lumping of complex systems were validated, important results in queuing theory and reliability theory were obtained, and a series of limit theorems for semi-Markov processes were proved by V. S. Korolyuk, academician of the NAS of Ukraine. He has also constructed the Poisson approximation for stochastic homogeneous additive functional with semi-Markov switching.
|
|
Points accumulation for imaging in nanoscale topography (PAINT) is a single-molecule localization method that achieves stochastic single-molecule fluorescence by molecular adsorption/absorption and photobleaching/desorption. The first dye used was Nile red which is nonfluorescent in aqueous solution but fluorescent when inserted into a hydrophobic environment, such as micelles or living cell walls. Thus, the concentration of the dye is kept small, at the nanomolar level, so that the molecule's sorption rate to the diffraction-limited area is in the millisecond region. The stochastic binding of single-dye molecules (probes) to an immobilized target can be spatially and temporally resolved under a typical widefield fluorescence microscope.
|
|
Diagram made by Antony Valentini in a lecture about the De Broglie–Bohm theory. Valentini argues quantum theory is a special equilibrium case of a wider physics and that it may be possible to observe and exploit quantum non- equilibrium Stochastic electrodynamics (SED) is an extension of the de Broglie–Bohm interpretation of quantum mechanics, with the electromagnetic zero-point field (ZPF) playing a central role as the guiding pilot-wave. The theory is a deterministic nonlocal hidden-variable theory. It is distinct from other more mainstream interpretations of quantum mechanics such as QED, a stochastic electrodynamics of the Copenhagen interpretation and Everett's many-worlds interpretation.
|
|
A related primal-dual technique for maximizing utility in a stochastic queueing network was developed by Stolyar using a fluid model analysis. The Stolyar analysis does not provide analytical results for a performance tradeoff between utility and queue size. A later analysis of the primal-dual method for stochastic networks proves a similar O(1/V), O(V) utility and queue size tradeoff, and also shows local optimality results for minimizing non-convex functions of time averages, under an additional convergence assumption. However, this analysis does not specify how much time is required for the time averages to converge to something close to their infinite horizon limits.
|
|
The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is another popular model for estimating stochastic volatility. It assumes that the randomness of the variance process varies with the variance, as opposed to the square root of the variance as in the Heston model. The standard GARCH(1,1) model has the following form for the variance differential: : d u_t = \theta(\omega - u_t)\,dt + \xi u_t\,dB_t \, The GARCH model has been extended via numerous variants, including the NGARCH, TGARCH, IGARCH, LGARCH, EGARCH, GJR-GARCH, etc. Strictly, however, the conditional volatilities from GARCH models are not stochastic since at time t the volatility is completely pre-determined (deterministic) given previous values.
|
|
Currently he is a Professor of Financial Mathematics at ETH Zürich. Soner co-authored a book, with Wendell Fleming, on viscosity solutions and stochastic control; Controlled Markov Processes and Viscosity Solutions (Springer-Verlag) in 1993, which was listed among the most-cited researcher in mathematics by Thomson Science in 2004. He authored or co-authored papers on nonlinear partial differential equations, viscosity solutions, stochastic optimal control and mathematical finance. He received the TÜBITAK-TWAS Science award in 2002, was the recipient of an ERC Advanced Investigators Grant in 2009 and the Alexander von Humboldt Foundation Research Award in 2014 and was elected as a SIAM Fellow in 2015.
|
|
A symmetric random walk and a Wiener process (with zero drift) are both examples of martingales, respectively, in discrete and continuous time. For a sequence of independent and identically distributed random variables X_1, X_2, X_3, \dots with zero mean, the stochastic process formed from the successive partial sums X_1,X_1+ X_2, X_1+ X_2+X_3, \dots is a discrete-time martingale. In this aspect, discrete-time martingales generalize the idea of partial sums of independent random variables. Martingales can also be created from stochastic processes by applying some suitable transformations, which is the case for the homogeneous Poisson process (on the real line) resulting in a martingale called the compensated Poisson process.
|
|
The Sethi model was developed by Suresh P. Sethi and describes the process of how sales evolve over time in response to advertising. The rate of change in sales depend on three effects: response to advertising that acts positively on the unsold portion of the market, the loss due to forgetting or possibly due to competitive factors that act negatively on the sold portion of the market, and a random effect that can go either way. Suresh Sethi published his paper "Deterministic and Stochastic Optimization of a Dynamic Advertising Model" in 1983. The Sethi model is a modification as well as a stochastic extension of the Vidale-Wolfe advertising model.
|
|
Louis Jean-Baptiste Alphonse Bachelier (; March 11, 1870 – April 28, 1946) was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, as part of his PhD thesis The Theory of Speculation (Théorie de la spéculation, published 1900). Bachelier's Doctoral thesis, which introduced the first mathematical model of Brownian motion and its use for valuing stock options, was the first paper to use advanced mathematics in the study of finance. Thus, Bachelier is considered as the forefather of mathematical finance and a pioneer in the study of stochastic processes.
|
|
The authors proposed a theoretical model (hereby named the ‘MRK model’ after the main proponents- Gita Mahmoudabadi, Govindan Rangarajan, and Prakash Kulkarni) which envisaged that because IDPs have multiple conformational states and rapid conformational dynamics, they are prone to engage in ‘promiscuous’ interactions. These stochastic interactions between the IDPs and their partners result in ‘noise’, defined as conformational noise. Indeed, many biological processes are driven by probabilistic events underscoring the importance of ‘noise’ in biological systems. However, while research on biological noise focused on low gene copy numbers as the predominant source of noise, noise arising from stochastic IDP interactions due to the conformational dynamics of IDPs had not been considered.
|
|
The most widely accepted model posits that the incidence of cancers due to ionizing radiation increases linearly with effective radiation dose at a rate of 5.5% per sievert. If this linear model is correct, then natural background radiation is the most hazardous source of radiation to general public health, followed by medical imaging as a close second. Other stochastic effects of ionizing radiation are teratogenesis, cognitive decline, and heart disease. Quantitative data on the effects of ionizing radiation on human health is relatively limited compared to other medical conditions because of the low number of cases to date, and because of the stochastic nature of some of the effects.
|
|
Performance Evaluation Process Algebra (PEPA) is a stochastic process algebra designed for modelling computer and communication systems introduced by Jane Hillston in the 1990s. The language extends classical process algebras such as Milner's CCS and Hoare's CSP by introducing probabilistic branching and timing of transitions. Rates are drawn from the exponential distribution and PEPA models are finite-state and so give rise to a stochastic process, specifically a continuous-time Markov process (CTMC). Thus the language can be used to study quantitative properties of models of computer and communication systems such as throughput, utilisation and response time as well as qualitative properties such as freedom from deadlock.
|
|
Xenakis also developed an stochastic synthesizer algorithm (used in GENDY), called dynamic stochastic synthesis, where a polygonal waveform's sectional borders' amplitudes and distance between borders may be generated using a form of random walk to create both aleatoric timbres and musical forms.Serra, 241. Further material may be generated by then refeeding the original waveform back into the function or wave forms may be superimposed. Elastic barriers or mirrors are used to keep the randomly generated values within a given finite interval, so as to not exceed limits such as the audible pitch range, avoid complete chaos (white noise), and to create a balance between stability and instability (unity and variety).
|
|
In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary but does not always have a trend. If the other roots of the characteristic equation lie inside the unit circle—that is, have a modulus (absolute value) less than one—then the first difference of the process will be stationary; otherwise, the process will need to be differenced multiple times to become stationary.
|
|
Nevertheless, when SDE is viewed as a continuous-time stochastic flow of diffeomorphisms, it is a uniquely defined mathematical object that corresponds to Stratonovich approach to a continuous time limit of a stochastic difference equation. In physics, the main method of solution is to find the probability distribution function as a function of time using the equivalent Fokker–Planck equation (FPE). The Fokker–Planck equation is a deterministic partial differential equation. It tells how the probability distribution function evolves in time similarly to how the Schrödinger equation gives the time evolution of the quantum wave function or the diffusion equation gives the time evolution of chemical concentration.
|
|
Wireless networks are sometimes best represented with stochastic models owing to their complexity and unpredictability, hence continuum percolation have been used to develop stochastic geometry models of wireless networks. For example, the tools of continuous percolation theory and coverage processes have been used to study the coverage and connectivity of sensor networks. One of the main limitations of these networks is energy consumption where usually each node has a battery and an embedded form of energy harvesting. To reduce energy consumption in sensor networks, various sleep schemes have been suggested that entail having a subcollection of nodes go into a low energy-consuming sleep mode.
|
|
Shades of gray produced by FM screening. Magnified version of the same image. Stochastic screening or FM screening is a halftone process based on pseudo- random distribution of halftone dots, using frequency modulation (FM) to change the density of dots according to the gray level desired. Traditional amplitude modulation halftone screening is based on a geometric and fixed spacing of dots, which vary in size depending on the tone color represented (for example, from 10 to 200 micrometres). The stochastic screening or FM screening instead uses a fixed size of dots (for example, about 25 micrometres) and a distribution density that varies depending on the color’s tone.
|
|
The survival probability is the probability that no jump has occurred in the interval . The change in the survival probability is :d p_s(t) = -p_s(t) h(t) \, dt. So :p_s(t) = \exp \left(-\int_0^t h(u) \, du \right). Let be a discontinuous stochastic process.
|
|
Individual op-amps can be screened for popcorn noise with peak detector circuits, to minimize the amount of noise in a specific application. Burst noise is modeled mathematically by means of the telegraph process, a Markovian continuous-time stochastic process that jumps discontinuously between two distinct values.
|
|
Journal Geology 92: 583–597. , using a computer simulation on hypothetical data sets, and by Rubel and Pak Rubel, M. and Pak, D.N. (1984) Theory of stratigraphic correlation by means of ordinal scales. Computers Geosciences 10:43–57.in terms of the formal logic and stochastic theory.
|
|
Stochastic roadmap simulation. is inspired by probabilistic roadmap. methods (PRM) developed for robot motion planning. The main idea of these methods is to capture the connectivity of a geometrically complex high-dimensional space by constructing a graph of local paths connecting points randomly sampled from that space.
|
|
"Investigating Data Theft with Stochastic Forensics". "Digital Forensics Magazine." been the subject of academic research,Nishide, T., Miyazaki, S., & Sakurai, K. (2012). "Security Analysis of Offline E-cash Systems with Malicious Insider". Journal of Wireless Mobile Networks, Ubiquitous Computing, and Dependable Applications, 3(1/2), 55-71.
|
|
In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution,A. Baddeley, I. Bárány, and R. Schneider. Spatial point processes and their applications. Stochastic Geometry: Lectures given at the CIME Summer School held in Martina Franca, Italy, September 13–18, 2004, pages 1–75, 2007.
|
|
Stochastic gradient descent is a popular algorithm for training a wide range of models in machine learning, including (linear) support vector machines, logistic regression (see, e.g., Vowpal Wabbit) and graphical models.Jenny Rose Finkel, Alex Kleeman, Christopher D. Manning (2008). Efficient, Feature-based, Conditional Random Field Parsing. Proc.
|
|
Peter Richtarik is a Slovak mathematician working in the area of big data optimization and machine learning, known for his work on randomized coordinate descent algorithms, stochastic gradient descent and federated learning. He is currently a Professor at the King Abdullah University of Science and Technology.
|
|
A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities.DLOUHÝ, M.; FÁBRY, J.; KUNCOVÁ, M.. Simulace pro ekonomy. Praha : VŠE, 2005. Realizations of these random variables are generated and inserted into a model of the system.
|
|
This article discussed alternative hypotheses, including a stochastic ordering (where the cumulative distribution functions satisfied the pointwise inequality ). This paper also computed the first four moments and established the limiting normality of the statistic under the null hypothesis, so establishing that it is asymptotically distribution-free.
|
|
On particularly busy freeways, a minor disruption may persist in a phenomenon known as traffic waves. A complete breakdown of organization may result in traffic congestion and gridlock. Simulations of organized traffic frequently involve queuing theory, stochastic processes and equations of mathematical physics applied to traffic flow.
|
|
He has made contributions to stochastic scheduling, Markov decision processes, queueing theory, the probabilistic analysis of algorithms, the theory of communications pricing and control, and Rendezvous Search Weber and his co-authors were awarded the 2007 INFORMS prize for their paper on the online bin packing algorithm.
|
|
The buffer acting component has been proposed to be relevant for neutralizing acid rain.Steve Cabaniss, Greg Madey, Patricia Maurice, Yingping Zhou, Laura Leff, Olacheesy head Bob Wetzel, Jerry Leenheer, and Bob Wershaw, comps, Stochastic Synthesis of Natural Organic Matter, UNM, ND, KSU, UNC, USGS, 22 Apr 2007.
|
|
The application of Markov random fields (MRF) for images was suggested in early 1984 by Geman and Geman.S. Geman and D. Geman (1984): "Stochastic relaxation, Gibbs Distributions and Bayesian Restoration of Images", IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 721–741, Vol. 6, No. 6.
|
|
W boson at CERN. From right to left: Carlo Rubbia, spokesperson of the UA1 experiment; Simon van der Meer, responsible for developing the stochastic cooling technique; Herwig Schopper, Director-General of CERN; Erwin Gabathuler, Research Director at CERN, and Pierre Darriulat, spokesperson of the UA2 experiment.
|
|
Another study employed a stochastic model to optimize the inventory management process at Spain-based retailer Zara: the new model increased sales by $275 million (3–4%) in 2007 and Zara continues to use the process for all of its products and at all retail locations.
|
|
In mathematics, the Paley–Wiener integral is a simple stochastic integral. When applied to classical Wiener space, it is less general than the Itō integral, but the two agree when they are both defined. The integral is named after its discoverers, Raymond Paley and Norbert Wiener.
|
|
He graduated in Physics at the University of Perugia and obtained his Ph.D. in physics from the University of Pisa in 1991 (S. Santucci advisor). His thesis was entitled "Stochastic Resonance". He is currently Professor at the Faculty of Science of the University of Perugia in Italy.
|
|
Risken (1984) However, d W_t / dt does not exist because the Wiener process is nowhere differentiable, and so the Langevin equation is, strictly speaking, only heuristic. In physics and engineering disciplines, it is nevertheless a common representation for the Ornstein–Uhlenbeck process and similar stochastic differential equations.
|
|
Hubbell introduced the neutral theory of ecology. Within the community (or metacommunity), species are functionally equivalent, and the abundance of a population of a species changes by stochastic demographic processes (i.e., random births and deaths). Equivalence of the species in the community leads to ecological drift.
|
|
Y. L. Le Coz and R. B. Iverson. A stochastic algorithm for high speed capacitance extraction in integrated circuits. Solid State Electronics, 35(7):1005-1012, 1992. Methods of truncating the discretization required by the FD and FEM approaches has greatly reduced the number of elements required.
|
|
The resulting power draw becomes higher than that required for other memories, e.g., spin-transfer torque memory (STT- RAM) or flash memory. Another challenge associated with Racetrack memory is the stochastic nature in which the domain walls move, i.e., they move and stop at random positions.
|
|
Proceedings Ninth IEEE International Conference on Computer Vision. that won the Marr Prize in ICCV 2003. In 2004, Zhu moved to high level vision by studying stochastic grammar. The grammar method dated back to the syntactic pattern recognition approach advocated by King-Sun Fu in the 1970s.
|
|
The single cell experiments used intracranial electrodes in the medial temporal lobe (the hippocampus and surrounding cortex). Modern development of concentration of measure theory (stochastic separation theorems) with applications to artificial neural networks give mathematical background to unexpected effectiveness of small neural ensembles in high-dimensional brain.
|
|
A number of types of stochastic processes have been considered that are similar to the pure random walks but where the simple structure is allowed to be more generalized. The pure structure can be characterized by the steps being defined by independent and identically distributed random variables.
|
|
The Doob-Meyer decomposition theorem is a theorem in stochastic calculus stating the conditions under which a submartingale may be decomposed in a unique way as the sum of a martingale and an increasing predictable process. It is named for Joseph L. Doob and Paul-André Meyer.
|
|
Grimm, V. and I. Storch. (2000). Minimum viable population size of capercaillie Tetrao Urogallus: results from a stochastic model. Wildlife Biology 6(4): 219–225. A demographic model based on Bavarian alpine populations of capercaillie suggest a minimum viable population size of the order of 500 birds.
|
|
A handicap in this process is the difficulty of seeing and manipulation at the nanoscale compared to the macroscale which makes deterministic selection of successful trials difficult; in contrast biological evolution proceeds via action of what Richard Dawkins has called the "blind watchmaker" Richard Dawkins, The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design, W. W. Norton; Reissue edition (September 19, 1996) comprising random molecular variation and deterministic reproduction/extinction. At present in 2007 the practice of nanotechnology embraces both stochastic approaches (in which, for example, supramolecular chemistry creates waterproof pants) and deterministic approaches wherein single molecules (created by stochastic chemistry) are manipulated on substrate surfaces (created by stochastic deposition methods) by deterministic methods comprising nudging them with STM or AFM probes and causing simple binding or cleavage reactions to occur. The dream of a complex, deterministic molecular nanotechnology remains elusive. Since the mid-1990s, thousands of surface scientists and thin film technocrats have latched on to the nanotechnology bandwagon and redefined their disciplines as nanotechnology.
|
|
Transitions from one precept to its alternative are called perceptual reversals. They are spontaneous and stochastic events that cannot be eliminated by intentional efforts, although some control over the alternation process is learnable. Reversal rates vary drastically between stimuli and observers. They are slower for people with bipolar disorder.
|
|
Springer Science & Business Media, 2013Liptser, Robert S., and Shiryaev, Albert N. Statistics of random processes II: Applications. 2nd ed. Vol. 6. Springer Science & Business Media, 2013. written together with Albert Shiryaev in 1974, has become internationally renowned reference textbook among scholars, working in stochastic analysis and related fields.
|
|
Dynamic stochastic general equilibrium modeling (abbreviated as DSGE, or DGE, or sometimes SDGE) is a method in macroeconomics that attempts to explain economic phenomena, such as economic growth and business cycles, and the effects of economic policy, through econometric models based on applied general equilibrium theory and microeconomic principles.
|
|
However, the statistical distribution of filesystems' metadata is affected by such large scale copying. By analyzing this distribution, stochastic forensics is able to identify and examine such data theft. Typical filesystems have a heavy tailed distribution of file access. Copying in bulk disturbs this pattern, and is consequently detectable.
|
|
M. Haenggi, J. Andrews, F. Baccelli, O. Dousse, and M. Franceschetti. Stochastic geometry and random graphs for the analysis and design of wireless networks. IEEE JSAC, 27(7):1029–1046, September 2009. The process is named after French mathematician Siméon Denis Poisson despite Poisson never having studied the process.
|
|
The focus of Biham's current research is on the development of computational methodologies for the simulation of stochastic processes in interstellar chemistry and in genetic networks. Biham is known for the Biham–Middleton–Levine traffic model, which is possibly the simplest model containing phase transitions and self-organization.
|
|
Robin Lyth Hudson received his Ph.D. from University of Oxford in 1966 under John Trevor Lewis with the Dissertation being Generalised Translation-Invariant Mechanics. He collaborated with K. R. Parthasarathy first in University of Manchester, and later at University of Nottingham, on their seminal work in quantum stochastic analysis.
|
|
The solution is then mapped back to the original domain with the inverse of the integral transform. There are many applications of probability that rely on integral transforms, such as "pricing kernel" or stochastic discount factor, or the smoothing of data recovered from robust statistics; see kernel (statistics).
|
|
Long term exposure to low level radiation is associated with stochastic health effects; the greater the exposure, the more likely the health effects are to occur. A group of doctors from the United States have called for a moratorium on hydraulic fracturing until health effects are more thoroughly studied.
|
|
Many networking and security companies claim to detect and control Skype's protocol for enterprise and carrier applications. While the specific detection methods used by these companies are often proprietary, Pearson's chi-squared test and stochastic characterization with Naive Bayes classifiers are two approaches that were published in 2007.
|
|
Several early stochastic models of wireless networks were based on Poisson point processes with the aim of studying the performance of slotted Aloha.R. Nelson and L. Kleinrock. The spatial capacity of a slotted aloha multihop packet radio network with capture. Communications, IEEE Transactions on, 32(6):684–694, 1984.
|
|
Some properties of stochastic models may be unusual for the users. Some outputs, especially those associated with transfers between statuses such as number of deaths, number of newly employed individuals etc., are “noised”. That corresponds to the observation of reality, but the users may be used to “smooth” results.
|
|
In the same year, Tang began her Ph.D. in theoretical computer science at the University of Washington under the supervision of James Lee. She pursued her research and generalized the above result, dequantizing other quantum machine learning HHL-based problems: principal component analysis and low-rank stochastic regression.
|
|
A related phenomenon is dithering applied to analog signals before analog-to-digital conversion. Stochastic resonance can be used to measure transmittance amplitudes below an instrument's detection limit. If Gaussian noise is added to a subthreshold (i.e., immeasurable) signal, then it can be brought into a detectable region.
|
|
Such considerations can motivate the consideration of a stochastic model even though the underlying system is governed by deterministic equations.Werndl, Charlotte (2009). Deterministic Versus Indeterministic Descriptions: Not That Different After All?. In: A. Hieke and H. Leitgeb (eds), Reduction, Abstraction, Analysis, Proceedings of the 31st International Ludwig Wittgenstein-Symposium.
|
|
A learning automaton is one type of machine learning algorithm studied since 1970s. Learning automata select their current action based on past experiences from the environment. It will fall into the range of reinforcement learning if the environment is stochastic and a Markov decision process (MDP) is used.
|
|
The species' natural habitats are high montane tepui environments. It is diurnal and usually found on open rock surfaces. It is a common species on the summit of Mount Roraima. There are currently no major threats, although the restricted range of the species makes its vulnerable to stochastic events.
|
|
These electrons increase the extent of chemical reactions in the resist. A secondary electron pattern that is random in nature is superimposed on the optical image. The unwanted secondary electron exposure results in loss of resolution, observable line edge roughness and linewidth variation. Stochastic aspect of EUV imaging.
|
|
P. De Bisschop and E. Hendrickx, Proc. SPIE 10583, 105831K (2018). This is related to shot noise , to be discussed further below. Due to the stochastic variations in arriving photon numbers, some areas designated to print actually fail to reach the threshold to print, leaving unexposed defect regions.
|
|
R package. Analysis of dichotomous and polytomous response data using unidimensional and multidimensional latent trait models under the Item Response Theory paradigm. Exploratory and confirmatory models can be estimated with quadrature (EM) or stochastic (MHRM) methods. Confirmatory bi-factor and two-tier analyses are available for modeling item testlets.
|
|
Real business cycle modelers sought to build macroeconomic models based on microfoundations of Arrow–Debreu general equilibrium. RBC models were one of the inspirations for dynamic stochastic general equilibrium (DSGE) models. DSGE models have become a common methodological tool for macroeconomists—even those who disagree with new classical theory.
|
|
There are model formulations for linear and nonlinear regression, robust estimation, discrete choice (including binary choice, ordered choice and unordered multinomial choice), censoring and truncation, sample selection, loglinear models, survival analysis, quantile regression (linear and count), panel data, stochastic frontier and data envelopment analysis, count data, and time series.
|
|
The requirement to not print constrains their use with low doses only. This could pose issues with stochastic effects.Stochastic Printing of Sub-Resolution Assist Features Hence their main application is to improve depth of focus for isolated features (dense features do not leave enough room for SRAF placement).
|
|
In 1978, Falmagne solved a well-known problem, posed in 1960 by the economists H.D. Block and Jacob Marschak in their article "Random Orderings and Stochastic Theories of Responses", concerning the representation of choice probabilities by random variables and published his findings in the Journal of Mathematical Psychology.
|
|
Her dissertation, Stochastic Differential Equations In A Hilbert Space, was supervised by Peter Falb. She then joined the faculty at Purdue University, but in 1971 moved to the University of Warwick. In 1977 she moved again, to the University of Groningen, where she remained until her 2006 retirement.
|
|
This has led to theories that gamma waves are associated with solving the binding problem. Gamma waves are observed as neural synchrony from visual cues in both conscious and subliminal stimuli. This research also sheds light on how neural synchrony may explain stochastic resonance in the nervous system.
|
|
The second prototype used stochastic fluidic reconfiguration and interconnection mechanism. Its 130 mm cubic modules weighed 1.78 kg each and made reconfiguration experiments excessively slow. The current third implementation inherits the fluidic reconfiguration principle. The lattice grid size is 80 mm, and the reconfiguration experiments are under way.
|
|
Any Stochastic Partial Information SPI(p), which can be considered as a solution of a linear inequality system, is called Linear Partial Information LPI(p) about probability p. It can be considered as an LPI-fuzzification of the probability p corresponding to the concepts of linear fuzzy logic.
|
|
The society publishes two journals, Bernoulli and Stochastic Processes and their Applications, and a newsletter, Bernoulli News. Additionally, it co-sponsors several other journals including Electronic Communications in Probability, Electronic Journal of Probability, Electronic Journal of Statistics, Probability Surveys, and Statistics Surveys.About the Bernoulli Society, retrieved 2014-06-23.
|
|
In mathematics, a Feller-continuous process is a continuous-time stochastic process for which the expected value of suitable statistics of the process at a given time in the future depend continuously on the initial condition of the process. The concept is named after Croatian-American mathematician William Feller.
|
|
A stochastic sample pattern is a random distribution of multisamples throughout the pixel. The irregular spacing of samples makes attribute evaluation complicated. The method is cost efficient due to low sample count (compared to regular grid patterns). Edge optimization with this method, although sub-optimal for screen aligned edges.
|
|
Neighbourhood components analysis is a supervised learning method for classifying multivariate data into distinct classes according to a given distance metric over the data. Functionally, it serves the same purposes as the K-nearest neighbors algorithm, and makes direct use of a related concept termed stochastic nearest neighbours.
|
|
In a different direction, with Anthony J. Pritchard (University of Warwick), he worked on concepts of stability radii and spectral value sets, building up a robustness theory covering deterministic and stochastic aspects of dynamical systems. After retiring in Germany, he is now a professor at Carlos III in Madrid.
|
|
Stochastic approximation is used when the function cannot be computed directly, only estimated via noisy observations. In this scenarios, this method (or family of methods) looks for the extrema of these function. The objective function would be:Powell, W. (2011). Approximate Dynamic Programming Solving the Curses of Dimensionality (2nd ed.
|
|
W. R. Young, A. J. Roberts, and G. Stuhne. Reproductive pair correlations and the clustering of organisms. Nature, 412:328–331, 2001. The macroscale may have to be treated as a stochastic system, but then the errors are likely to be much larger and the closures more uncertain.
|
|
In the 2010 Oakland freeway shootout, Byron Williams was said to be en route to offices of the American Civil Liberties Union and the Tides Foundation, planning to commit mass murder, "indirectly enabled by the conspiracy theories" of Glenn Beck and Alex Jones. As a left-wing example, they cite the 2012 shooting incident at the headquarters of the Family Research Council. The stochastic terrorism model is a stochastic process, a random, model of those terror attacks intended by the random nature of their timing and targets to excite a generalized fear. Nonetheless, lone wolf terrorists are "indirectly enabled by the conspiracy theories" circulated in the mass media, especially by high status political or religious leaders.
|
|
Richtarik's early research concerned gradient-type methods, optimization in relative scale, sparse principal component analysis and algorithms for optimal design. Since his appointment at Edinburgh, he has been working extensively on building algorithmic foundations of randomized methods in convex optimization, especially randomized coordinate descent algorithms and stochastic gradient descent methods. These methods are well suited for optimization problems described by big data and have applications in fields such as machine learning, signal processing and data science. Richtarik is the co-inventor of an algorithm generalizing the randomized Kaczmarz method for solving a system of linear equations, contributed to the invention of federated learning, and co-developed a stochastic variant of the Newton's method.
|
|
Inconclusive but encouraging experiments were carried out in 2012 by Dmitriyeva and Moddel in which emissions in "... infrared was clearly observed" which they could not explain using "...conventional thermodynamic models". In 2013 Auñon et al. showed that Casimir and Van der Waals interactions are a particular case of stochastic forces from electromagnetic sources when the broad Planck's spectrum is chosen and the wavefields are non-correlated. Addressing fluctuating partially coherent light emitters with a tailored spectral energy distribution in the optical range, this establishes the link between stochastic electrodynamics and coherence theory; henceforth putting forward a way to optically create and control both such zero-point fields as well as Lifshitz forces E. M. Lifshitz, Dokl. Akad.
|
|
The convection–diffusion equation (with no sources or drains, ) can be viewed as a stochastic differential equation, describing random motion with diffusivity and bias . For example, the equation can describe the Brownian motion of a single particle, where the variable describes the probability distribution for the particle to be in a given position at a given time. The reason the equation can be used that way is because there is no mathematical difference between the probability distribution of a single particle, and the concentration profile of a collection of infinitely many particles (as long as the particles do not interact with each other). The Langevin equation describes advection, diffusion, and other phenomena in an explicitly stochastic way.
|
|
The von Kármán wind turbulence model (also known as von Kármán gusts) is a mathematical model of continuous gusts. It matches observed continuous gusts better than that Dryden Wind Turbulence Model and is the preferred model of the United States Department of Defense in most aircraft design and simulation applications. The von Kármán model treats the linear and angular velocity components of continuous gusts as spatially varying stochastic processes and specifies each component's power spectral density. The von Kármán wind turbulence model is characterized by irrational power spectral densities, so filters can be designed that take white noise inputs and output stochastic processes with the approximated von Kármán gusts' power spectral densities.
|
|
For stronger signal amplitudes that stimulated the interneurons in the presence of no noise, however, the addition of noise always decreased the mutual information transfer demonstrating that stochastic resonance only works in the presence of low-intensity signals. The information carried in each spike at different levels of input noise was also calculated. At the optimum level of noise, the cells were more likely to spike, resulting in spikes with more information and more precise temporal coherence with the stimulus. Stochastic resonance is a possible cause of escape behavior in crickets to attacks from predators that cause pressure waves in the tested frequency range at very low amplitudes, like the wasp Liris niger.
|
|
An aspect of stochastic resonance that is not entirely understood has to do with the relative magnitude of stimuli and the threshold for triggering the sensory neurons that measure them. If the stimuli are generally of a certain magnitude, it seems that it would be more evolutionarily advantageous for the threshold of the neuron to match that of the stimuli. In systems with noise, however, tuning thresholds for taking advantage of stochastic resonance may be the best strategy. A theoretical account of how a large model network (up to 1000) of summed FitzHugh–Nagumo neurons could adjust the threshold of the system based on the noise level present in the environment was devised.
|
|
In 1933 Andrei Kolmogorov published in German, his book on the foundations of probability theory titled Grundbegriffe der Wahrscheinlichkeitsrechnung, where Kolmogorov used measure theory to develop an axiomatic framework for probability theory. The publication of this book is now widely considered to be the birth of modern probability theory, when the theories of probability and stochastic processes became parts of mathematics. After the publication of Kolmogorov's book, further fundamental work on probability theory and stochastic processes was done by Khinchin and Kolmogorov as well as other mathematicians such as Joseph Doob, William Feller, Maurice Fréchet, Paul Lévy, Wolfgang Doeblin, and Harald Cramér. Decades later Cramér referred to the 1930s as the "heroic period of mathematical probability theory".
|
|
The word stochastic in English was originally used as an adjective with the definition "pertaining to conjecturing", and stemming from a Greek word meaning "to aim at a mark, guess", and the Oxford English Dictionary gives the year 1662 as its earliest occurrence. In his work on probability Ars Conjectandi, originally published in Latin in 1713, Jakob Bernoulli used the phrase "Ars Conjectandi sive Stochastice", which has been translated to "the art of conjecturing or stochastics". This phrase was used, with reference to Bernoulli, by Ladislaus Bortkiewicz who in 1917 wrote in German the word stochastik with a sense meaning random. The term stochastic process first appeared in English in a 1934 paper by Joseph Doob.
|
|
It can be defined such that its index set is the real line, and this stochastic process is also called the stationary Poisson process. If the parameter constant of the Poisson process is replaced with some non-negative integrable function of t, the resulting process is called an inhomogeneous or nonhomogeneous Poisson process, where the average density of points of the process is no longer constant. Serving as a fundamental process in queueing theory, the Poisson process is an important process for mathematical models, where it finds applications for models of events randomly occurring in certain time windows. Defined on the real line, the Poisson process can be interpreted as a stochastic process, among other random objects.
|
|
1981: Mathematical Methods in Social Science, Chichester: John Wiley and Sons. 11\. 1982: Stochastic Models for Social Processes, Chichester 3rd edition: John Wiley and Sons. 12\. 1985: Russian translation of Chapters 1–8 of Stochastic Models for Social Processes, 3rd edition, Moscow. 13\. 1984: God of Chance, London: SCM Press, Italian translation, 1987. 14\. 1987: Latent Variable Models and Factor Analysis, London: Griffin. 15\. 1991: & A. F. Forbes and S.I. McClean, Statistical Techniques for Manpower Planning, Chichester 2nd edition: John Wiley and Sons (Hebrew translation 2001, The Open University of Israel). 16\. 1993: & K.Haagen & M.Deistler (eds.), Statistical Modelling and Latent Variables, Amsterdam: North-Holland. 17\. 1996: Uncertain Belief, Oxford: The Clarendon Press. 18\.
|
|
The application of radiation can aid the patient by providing doctors and other health care professionals with a medical diagnosis, but the exposure of the patient should be reasonably low enough to keep the statistical probability of cancers or sarcomas (stochastic effects) below an acceptable level, and to eliminate deterministic effects (e.g. skin reddening or cataracts). An acceptable level of incidence of stochastic effects is considered to be equal for a worker to the risk in other radiation work generally considered to be safe. This policy is based on the principle that any amount of radiation exposure, no matter how small, can increase the chance of negative biological effects such as cancer.
|
|
He made original contributions on system identification, including the estimation of the orders, time-delays and parameters of stochastic systems. He gave a criterion for time-delay estimate, with which one can get a strong consistent time-delay estimate. He with co- authors initiated the research on the parameter identification and adaptive control of the systems with quantized observations, and investigated the optimal adaptive control and identification errors, time complexity, optimal input design, and impact of disturbances and unmodeled dynamics on identification accuracy and complexity in both stochastic and deterministic frameworks. With a series of significant results, he has established a solid framework for the identification and adaptive control of uncertainty systems with quantized information.
|
|
More specifically, for any given level of metabolic cost, there is an optimal trade-off between noise and processing speed and increasing the metabolic cost leads to better speed-noise trade-offs. A recent work proposed a simulator (SGNSim, Stochastic Gene Networks Simulator), that can model GRNs where transcription and translation are modeled as multiple time delayed events and its dynamics is driven by a stochastic simulation algorithm (SSA) able to deal with multiple time delayed events. The time delays can be drawn from several distributions and the reaction rates from complex functions or from physical parameters. SGNSim can generate ensembles of GRNs within a set of user-defined parameters, such as topology.
|
|
Zivin, Just, and Zilberman (2006)Graff Zivin, J, R Just, and D Zilberman, “Risk Aversion, Liability Rules, and Safety,” International Review of Law and Economics, 4(2006): 604-623. investigates the Coase theorem under stochastic externality. Ronald Coase famously won the Nobel prize for his work claiming that a competitive system with well-defined property right assignments, perfect information, and zero transaction costs would attain Pareto optimality through a process of voluntary bargaining and side payments. This paper investigates this claim in the context of a stochastic externality problem and finds that, when at least one agent is risk averse, optimal outcomes are not independent of the initial assignment of property rights.
|
|
The paper demonstrated that in static Arrow-Debreu economies with complete markets, extrinsic uncertainty (where no fundamentals of the model are stochastic) cannot matter to equilibrium allocations. They then showed that when some agents were restricted in their trades, so that market completeness was violated, sunspots could matter, i.e. there could exist rational expectations equilibria in which equilibrium prices depended on the realization of an extrinsic stochastic process. In passing, they made the observation that since the validity of the first welfare theorem implied that there could be no sunspot equilibria, a necessary condition for the existence of such equilibria was a violation of the conditions under which the first welfare theorem holds.
|
|
Differential equations describe changes in molecular concentrations over time in a deterministic manner. Simulations based on differential equations usually do not attempt to solve those equations analytically, but employ a suitable numerical solver. The stochastic Gillespie algorithm changes the composition of pools of molecules through a progression of randomness reaction events, the probability of which is computed from reaction rates and from the numbers of molecules, in accordance with the stochastic master equation. In population- based approaches, one can think of the system being modeled as being in a given state at any given time point, where a state is defined according to the nature and size of the populated pools of molecules.
|
|
Her particular areas of research have been in measure- valued processes (especially superprocesses and their generalisations); in theoretical population genetics; and in mathematical ecology. A recent focus has been on the genetics of spatially extended populations, where she has exploited and developed inextricable links with infinite-dimensional stochastic analysis. Her resolution of the so-called 'pain in the torus' is typical of her work in that it draws on ideas from diverse areas, from measure-valued processes to image analysis. The result is a flexible framework for modelling biological populations which, for the first time, combines ecology and genetics in a tractable way, while introducing a novel and mathematically interesting class of stochastic processes.
|
|
Nicolai Vladimirovich Krylov (; born 5 June 1941) is a Russian mathematician specializing in partial differential equations, particularly stochastic partial differential equations and diffusion processes. Krylov studied at Lomonosov University, where he in 1966 under E. B. Dynkin attained a doctoral candidate title (similar to a PhD) and in 1973 a Russian doctoral degree (somewhat more prestigious than a PhD). He taught from 1966 to 1990 at the Lomonosov University and is since 1990 a professor at the University of Minnesota. At the beginning of his career (starting from 1963) he, in collaboration with Dynkin, worked on nonlinear stochastic control theory, making advances in the study of convex,The non-linearity can be modeled by a convex function.
|
|
Kalman developed the study of the time domain using state- space models. Joining Kalman, Ho showed that the state-space representation provides a convenient and compact way to model and analyze dynamical systems with multiple inputs and outputs which would otherwise take multiple Laplace transforms to encode; further, the state-space representation can be extended into nonlinear systems. Their paper controllability of linear dynamic systems, developed the theory of controllability (then known as the "Kalman-Bertram condition"). Together with Ho's student Robert Lee at MIT, the paper A Bayesian approach to problems in stochastic estimation and control formulated a general class of stochastic estimation and control problems from a Bayesian Decision-Theoretic viewpoint.
|
|
Concretely, the integral from 0 to any particular t is a random variable, defined as a limit of a certain sequence of random variables. The paths of Brownian motion fail to satisfy the requirements to be able to apply the standard techniques of calculus. So with the integrand a stochastic process, the Itô stochastic integral amounts to an integral with respect to a function which is not differentiable at any point and has infinite variation over every time interval. The main insight is that the integral can be defined as long as the integrand H is adapted, which loosely speaking means that its value at time t can only depend on information available up until this time.
|
|
In mathematical finance, the described evaluation strategy of the integral is conceptualized as that we are first deciding what to do, then observing the change in the prices. The integrand is how much stock we hold, the integrator represents the movement of the prices, and the integral is how much money we have in total including what our stock is worth, at any given moment. The prices of stocks and other traded financial assets can be modeled by stochastic processes such as Brownian motion or, more often, geometric Brownian motion (see Black–Scholes). Then, the Itô stochastic integral represents the payoff of a continuous-time trading strategy consisting of holding an amount Ht of the stock at time t.
|
|
These methods use stochastic optimization, specifically stochastic dynamic programming to find the shortest path in networks with probabilistic arc length. The concept of travel time reliability is used interchangeably with travel time variability in the transportation research literature, so that, in general, one can say that the higher the variability in travel time, the lower the reliability would be, and vice versa. In order to account for travel time reliability more accurately, two common alternative definitions for an optimal path under uncertainty have been suggested. Some have introduced the concept of the most reliable path, aiming to maximize the probability of arriving on time or earlier than a given travel time budget.
|
|
This was first shown in a synthetic transcription network and later on in the natural context in the SOS DNA repair system of E .coli. The second function is increased stability of the auto-regulated gene product concentration against stochastic noise, thus reducing variations in protein levels between different cells.
|
|
It has been argued that the Rasch model is a stochastic variant of the theory of conjoint measurement (e.g., ; ; ; ; ; ), however, this has been disputed (e.g., Karabatsos, 2001; Kyngdon, 2008). Order restricted methods for conducting probabilistic tests of the cancellation axioms of conjoint measurement have been developed in the past decade (e.g.
|
|
On the real line, the Poisson process is a type of continuous-time Markov process known as a birth process, a special case of the birth–death process (with just births and zero deaths).A. Papoulis and S. U. Pillai. Probability, random variables, and stochastic processes. Tata McGraw-Hill Education, 2002.
|
|
The basic idea of the MCAM is to approximate the original controlled process by a chosen controlled markov process on a finite state space. In case of need, one must as well approximate the cost function for one that matches up the Markov chain chosen to approximate the original stochastic process.
|
|
In physics, Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems. It was originally developed by French physicist Paul Langevin. The approach is characterized by the use of simplified models while accounting for omitted degrees of freedom by the use of stochastic differential equations.
|
|
Although models based on these and other point processes come closer to resembling reality in some situations, for example in the configuration of cellular base stations,A. Guo and M. Haenggi. Spatial stochastic models and metrics for the structure of base stations in cellular networks. IEEE Transactions on Wireless Communications, vol.
|
|
In finance, the Heston model, named after Steven Heston, is a mathematical model describing the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a model assumes that the volatility of the asset is not constant, nor even deterministic, but follows a random process.
|
|
These systems are mostly deterministic, and the influence of thermal fluctuations can be neglected. However, this does not include living nature. Biological systems have active components (genetic networks, protein networks, molecular motors, neurons), which consist of discrete units (i. e. cells) and require the consideration of stochastic processes (thermal noise).
|
|
The two main forces threatening D. herbstobatae are habitat destruction, especially by wildfire, and introduced species, particularly feral hogs and goats. Stochastic events in the small populations that make up the species include environmental threats such as invasion of the habitat by tourists and catastrophes such as fire and landslides.
|
|
However, by combining roulette-wheel selection with the cloning of the best program of each generation, one guarantees that at least the very best traits are not lost. This technique of cloning the best-of-generation program is known as simple elitism and is used by most stochastic selection schemes.
|
|