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Topic: Stochastic process

Related Topics

Probability distribution

Gaussian stochastic process

Gaussian process

Random variable

Poisson process

Markov property

Stochastic calculus

Martingale theory

Markov chain

Branching process

Bernoulli process

Wiener process

Measure theory

Random sequence

Probability space

	Stochastic process - Wikipedia, the free encyclopedia
		A stochastic process is a random function, that is a random variable X defined on a probability space (Ω, Pr) with values in a space of functions F.
		Stochastic processes may be defined in higher dimensions by attaching a multivariate random variable to each point in the index set, which is equivalent to using a multidimensional index set.
		The paradigm continuous stochastic process is that of the Wiener process.
	en.wikipedia.org /wiki/Stochastic_process (1378 words)

	NationMaster - Encyclopedia: Stochastic process
		A point process is a type of stochastic process that is widely used in many fields of applied mathematics, such as queueing theory and computational neuroscience.
		The Galton-Watson process is a stochastic process arising from Francis Galtons statistical investigation of the extinction of surnames.
		In statistics, a stochastic process is often known as a time series, where the index set is a finite (or at most countable) ordered sequence of real numbers.
	www.nationmaster.com /encyclopedia/Stochastic-process (3499 words)

	PlanetMath: stochastic process
		In a random process, the index set may not be linearly ordered, as in the case of a random field, where the index set may be, for example, the unit sphere
		This is version 7 of stochastic process, born on 2004-09-28, modified 2006-02-24.
		Assume that the process is time-homogenous and that the transition rate from state 0 to state 1 is mean1 state 0 to state 2 is mean2.
	planetmath.org /encyclopedia/StochasticProcess.html (394 words)

	Science Fair Projects - Stochastic process
		In practical applications, the domain over which the function is defined is a time interval (a stochastic process of this kind is called a time series in applications) or a region of space (a stochastic process being called a random field).
		The paradigm continuous stochastic process is that of Brownian motion.
		Thus the random force is described by a two component stochastic process; two real-valued random variables are associated to each point in the index set, time, (note that since the liquid is viewed as being homogeneous the force is independent of the spatial coordinates) with the domain of the two random variables being
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Stochastic_process (1545 words)

	Definition of Stochastic
		A stochastic process is one whose behavior is non-deterministic in that the next state of the environment is not fully determined by the previous state of the environment.
		In mathematics, specifically in probability theory, the field of stochastic processes has for some decades been a major area of research, to which hundreds of researchers have devoted their careers.
		Stochastic music was pioneered by Iannis Xenakis, who used probability, game theory, group theory, set theory, and Boolean algebra, and frequently used computers to produce his scores.
	www.wordiq.com /definition/Stochastic (570 words)

	Stochastic process (Site not responding. Last check: 2007-11-06)
		The domain D becomes the index set of the stochastic process, and a particular stochastic process is determined by specifying the joint probability distributions of the various random variables f''(''x).
		Note, however, that the definition of stochastic process as an indexed collection of random variables is much more general than the case where the indices are points of the domain of the random function.
		Markov process es are those in which the future is conditionally independent of the past given the present.
	www.serebella.com /encyclopedia/article-Stochastic_process.html (2208 words)

	Time Series Analysis, Stochastic Process (Site not responding. Last check: 2007-11-06)
		While it is possible that the terms of a stochastic process might be IID—in which case, time series analysis reduces to statistics—this is not a particularly interesting case.
		From white noise processes can be constructed moving average, autoregressive and autoregressive-moving-average processes, which are generally used to model conditionally homoskedastic autocorrelated processes.
		Brownian motion A simple continuous stochastic process that is widely used in physics and finance for modeling random behavior that evolves over time.
	www.riskglossary.com /articles/time_series_stochastic_process.htm (1195 words)

	Stochastic process (Site not responding. Last check: 2007-11-06)
		In practical applications the domain over the function is defined is a time (a stochastic process of this kind is a time series in applications) or a region of (a stochastic process being called a random field).
		The domain D becomes the index set of the process and a particular stochastic process is by specifying the joint probability distributions of various random variables f (x).
		Gaussian processes : processes where all linear combinations of are normally distributed random variables.
	www.freeglossary.com /Stochastic_processes (1846 words)

	Markov process - Wikipedia, the free encyclopedia
		In probability theory, a Markov process is a stochastic process characterized as follows: The state c
		Under the assumption that the process runs only from time 0 to time N and that the initial and final states are known, the state sequence is then represented by a finite vector C = (c
		This process would be known as a first-order Markov process.
	en.wikipedia.org /wiki/Markov_process (186 words)

	Dome Printing Stochastic or FM Screening Process
		Stochastic used to be an idea ahead of its time - 10 years ago.
		While the dots used in conventional halftone printing are equally spaced in a rigid pattern, the dots used in the Staccato process are not.
		The Staccato process varies the dots by density and frequency according to the tone value reproduced.
	www.domeprinting.com /html/technology.html (514 words)

	Mathmas
		Along with quantum theory, the theory of stochastic processes is the mathematical foundation of modern physics.
		We will apply the theory of stochastic processes to study the collective behavior of groups of robots.
		A generalized Markov process is a stochastic process whose value at time t+1 depends not only on its value at time t, but also on its values at time t-1… t-m.
	www.isi.edu /~lerman/projects/mathmas/mathmas.html (1183 words)

	Mean Reversion (Site not responding. Last check: 2007-11-06)
		Mean reversion is a tendency for a stochastic process to remain near, or tend to return over time to a long-run average value.
		Mean reversion is a tendency for a stochastic process to remain near, or return over time to a long-run average.
		Usually, a decision to model a quantity with a mean reverting stochastic process is based both on empirical observation of that quantity over time, as well as some theoretical argument as to why it should be mean reverting.
	www.riskglossary.com /articles/mean_reversion.htm (256 words)

	Stochastic Processes (Site not responding. Last check: 2007-11-06)
		This popular model is the most used stochastic process in financial economics theory and in the practice.
		The stochastic process of V, geometric Brownian motion (GBM), means that this variable follows a lognormal process over time with the following parameters.
		The ease of using irregularly sampled data is one of the greatest advantages of continuous-time stochastic processes, by the econometric point of view.
	www.puc-rio.br /marco.ind/stochast.html (1792 words)

	Stochastic process (Site not responding. Last check: 2007-11-06)
		A stochastic process is a random function, that is a random variable X defined on a probability space (Ω, Pr) with values in a space of functions F.
		Focus is on stochastic modelling in the physical and engineering sciences, with particular emphasis on queueing theory, reliability theory, inventory theory, simulation, stochastic control theory and probabilistic networks and graphs.
		It defines the stages in the standardization process, the requirements for moving a document between stages and the types of documents used during this process.
	www.omniknow.com /common/wiki.php?in=en&term=Random_process (2869 words)

	Stochastic Process (Site not responding. Last check: 2007-11-06)
		The majority of its work is produced using 20 micron stochastic to achieve the...
		America is in the process of stopping any more buying of crude oil in...
		The stochastic models, the open interest model and price acceleration models are pointing...
	www.wikiverse.org /stochastic-process (1706 words)

	Stochastic Process Modeling (Site not responding. Last check: 2007-11-06)
		A stochastic process is any process that shows probabilistic behavior that ``evolves in time'' [4].
		Therefore, a stochastic process is a collection of random variables that are ordered in time.
		In modeling a stochastic process, we must first remove the time dependent behavior of the statistical metrics by partitioning the data or by some other means (see Section 2.2.5).
	ei.cs.vt.edu /~williams/VideoTraffic/node13.html (197 words)

	SIGNAL: Stochastic process algebra for biochemical signalling pathways analysis
		The stochastic process algebra PEPA is well-established as a formalism for performance modelling of computer and communication systems.
		In this talk I will use the stochastic process algebra PEPA, and the model checker PRISM, to develop and analyse a number of novel, predictive models for parts of the ERK pathway (this pathway plays an important role in cancer).
		Several case studies on biological process modelling have been conducted with the PRISM Probabilistic Model-Checker, applying process calculi and probabilistic model checking technology to the study of biological processes.
	homepages.inf.ed.ac.uk /stg/research/SIGNAL (1063 words)

	Performance TOOLS'98: Tutorial 1
		Stochastic Process Algebras (SPA) have emerged over the last decade as an exciting new approach to performance modelling.
		Her research work is largely focussed on the stochastic process algebra, PEPA; in particular, investigating the ways in which the structure imposed by the process algebra can be exploited in the underlying stochastic model when it is solved to derive the performance characteristics.
		This is now being extended to consider stochastic elements of such models, through the use of stochastic process algebras, such as PEPA.
	www.uib.es /tools98/tutorial1.html (818 words)

	Extra Problems for Chapter 4
		Thus the dependence between adjacent n-blocks of a stationary process does not grow linearly with n.
		be the entropy rate of the Y process (the sequence of coin tosses).
		Suppose we observe one of two stochastic processes but don't know which.
	www-isl.stanford.edu /~jat/eit2/webbook/exch4/exch4.html (225 words)

	[No title]
		One topic of research is the development of inference procedures for a stochastic process that models the spatial interrelation of point locations.
		Let the signal be further abstracted to a "grain-germ" stochastic process, where the germs are the locations of the grains (mines).
		Statistical image processing yields an estimate of the signal; then inference on the resulting stochastic processes (including the underlying point process) consists of estimating and testing associated parameters that determine whether a minefield is present or not.
	www.ee.iastate.edu /~davidson/jdresearch.html (561 words)

	Stochastic Processes
		A stochastic process involves a random element and a time element.
		A counting process is discrete, taking only integer values; the size of an insurance claim is treated as continuous.
		In general a filtration need not be generated by a single process: it may contain the histories of many processes at once.
	www.staff.city.ac.uk /r.j.gerrard/courses/2dsm/dsm03_2.htm (341 words)

	Wilmott Forums - What is adaptedness of a stochastic process?
		There are many different measures and process can be measurable (or not) with respect to, and many filtrations that a process can be adapted (or not) with respect to.
		An example of a non-adapted, non-measurable process is a random walk in which the variance at time t is equal to the lowest integer b such that t = a/b.
		the basic problem of stochastic calculus is that the measure is defined on the space of paths which are functions of time.
	www.wilmott.com /messageview.cfm?catid=8&threadid=6640 (481 words)

	Towards Model Checking Stochastic Process Algebra - Hermanns, Katoen, Meyer-Kayser (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling.
		However, analysis of stochastic process algebra models is state-oriented, because standard numerical analysis is typically based on the calculation of (transient and steady) state probabilities.
		27 Stochastic process algebras as a tool for performance and de..
	citeseer.ist.psu.edu /344073.html (711 words)

	Wiener Process (Site not responding. Last check: 2007-11-06)
		Processes with this property are called Markov processes.
		Stationary Markov processes are of special interest, in particular for describing equilibrium fluctuations.
		means the random processes on both sides of the equality have the same distribution.
	www.met.rdg.ac.uk /~swr02klh/phd/mamaos/node11.html (123 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		A stochastic process is a function of two variables: t (time parameter) and ((probability parameter).
		If the random variables xt are discrete the stochastic process has a discrete state space.
		If the random variables xt are continuous, the stochastic process has a continuous state space.
	iweb.tntech.edu /fhossain/CEE6430/LECTURE19.doc (683 words)

	Citations: Bisimulation Algorithms for Stochastic Process Algebras and Their BDD-based Implementation - Hermanns, ... (Site not responding. Last check: 2007-11-06)
		The bisimilar quotient of component k has state space = f 0; n k 1 g, and is characterized by matrices W k;e 2 R n k n k de ned....
		Hermanns, M. Siegle, Bisimulation algorithms for stochastic process algebras and their BDD-based implementation, in: J.P. Katoen (Ed.), Proceedings of the ARTS'99, Lecture Notes in Computer Science, vol.
		....for non stochastic process algebras and for the purely Markovian case.
	citeseer.ist.psu.edu /context/869896/390309 (2861 words)

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