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Topic: Markov process

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	Markov chain - Wikipedia, the free encyclopedia
		Markov chains are related to Brownian motion and the ergodic hypothesis, two topics in physics which were important in the early years of the twentieth century, but Markov appears to have pursued this out of a mathematical motivation, namely the extension of the law of large numbers to dependent events.
		Markov chains also have many applications in biological modelling, particularly population processes, which are useful in modelling processes that are (at least) analogous to biological populations.
		Markov processes can also be used to generate superficially "real-looking" text given a sample document: they are used in various pieces of recreational "parody generator" software (see dissociated press, Jeff Harrison, Mark V Shaney or [1]).
	en.wikipedia.org /wiki/Markov_chain (1800 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)

	Markov, Andrei Andreyevich - Hutchinson encyclopedia article about Markov, Andrei Andreyevich
		Markov's early work was devoted primarily to number theory – continued fractions, approximation theory, differential equations, integration in elementary equations – and to the problem of moments and probability theory.
		A Markov chain may be described as a chance process that possesses a special property, so that its future may be predicted from the present state of affairs just as accurately as if the whole of its past history were known.
		Markov believed that the only real examples of his chains were to be found in literary texts, and he illustrated his discovery by calculating the alteration of vowels and consonants in Pushkin's Eugene Onegin.
	encyclopedia.farlex.com /Markov,+Andrei+Andreyevich (259 words)

	Markov chain : Markov process
		Markov chains are used to model various processes in queuing theory and statistics, and can also be used as a signal model in entropy coding techniques such as arithmetic coding.
		Markov chains also have many biological applications, particularly population processes, which are useful in modelling processes that are (at least) analogous to biological populations.
		Markov processes can also be used to generate superficially "real-looking" text given a sample document: they are used in various pieces of recreational "parody generator" software (see Jeff Harrison).
	www.fastload.org /ma/Markov_process.html (316 words)

	Markov
		Markov processes are represented graphically using state transition diagrams like the one shown in the class handout.
		A discrete Weiner random process is a random walk process with p=q=0.5, and is known as binary white noise.
		The process is a Markov process since (a) the current value of the process depends on the previous value, and (b) the magnitude of the change in the process is Gaussian with the change being +ve or -ve with equal probability.
	www.engr.udayton.edu /faculty/mdaniels/htm315/Markov.htm (1816 words)

	Markov Explanation
		A Markov analysis looks at a sequence of events, and analyzes the tendency of one event to be followed by another.
		A Markov Chain, while similar to the source in the small, is often nonsensical in the large.
		Markov processes have been used to generate music as early as the 1950's by Harry F. Olson at Bell Labs.
	www.doctornerve.org /nerve/pages/interact/markhelp.htm (731 words)

	Markov Chain Software, Markov Process & Model - Relex Markov Feature Article
		Markov processes are a special class of stochastic processes that uniquely determine the future behavior of the process by its present state.
		Thus, the basic assumption of a Markov process is that the behavior of the system in each state is memoryless.
		Because of constant transition rate restriction, the Homogenous Markov process should not be used to model the behavior of systems that are subjected to component wear-out characteristics.
	www.relex.com /resources/art/art_markov1.asp (966 words)

	Markov process (Site not responding. Last check: 2007-10-08)
		Informally, a stochastic process has the Markovproperty if "the future depends only on the present, not on the past"; that is, if the probability distribution of future states of the processdepends only upon the current state, and conditionally independent of the past states (the path of the process) giventhe present state.
		A process with the Markov property is usually called a Markov process, and may be describedas Markovian.
		The most famous Markov processes are Markov chains, but many otherprocesses, including Brownian motion, are Markovian.
	www.therfcc.org /markov-process-140253.html (189 words)

	Hidden Markov Models
		In computing, such processes, if they are reasonably complex and interesting, are usually called Probabilistic Finite State Automata (PFSA) or Probabilistic Finite State Machines (PFSM) because of their close links to deterministic and non-deterministic finite state automata as used in formal language theory.
		Examples are (hidden) Markov Models of biased coins and dice, formal languages, the weather, etc.; Markov models and Hidden Markov Models (HMM) are used in Bioinformatics to model DNA and protein sequences.
		The order of a Markov model of fixed order, is the length of the history or context upon which the probabilities of the possible values of the next state depend.
	www.csse.monash.edu.au /~lloyd/tildeMML/Structured/HMM.html (1021 words)

	Stochastic Processes and Queuing Models, Queueing Theory - Numericana
		Simulating a poisson process is easy with a uniform random number generator.
		Although one could consider modulated Markov chains (whose transition matrices vary with n) Markov processes are usually understood to be stationary unless otherwise specified (their transition probabilities are constant).
		For such a process, a generator matrix Q is defined (also called a transition rate matrix) as the time derivative of the stochastic matrix that gives the probability of ending up in state j at time t, starting from state i at time 0.
	home.att.net /~numericana/answer/stochastic.htm (1679 words)

	Markov Process (Site not responding. Last check: 2007-10-08)
		Asymptotic behaviour of a reversible Markov process of polymerization...
		DC MetaData pour: Recurrent extensions of self-similar Markov processes and Cram...
		Markov processes and a multiple generating function of product of generalized La...
	www.scienceoxygen.com /math/591.html (304 words)

	IDM : Markov Chains : Concept and Implications.
		It is important to recognise that the lack of memory in Markov chains is identical to the lack of memory in primitive genetic programs where there is no sensitivity to feedback from the context.
		Reflecting on the requirement that Markov chains have no memory, it become apparent that any form of consciousness would be at best 'fleeting'; perhaps a sort of 'awareness' that cannot go past the moment.
		We see a form of this in territorial mappings where the sequence method is used in the form of waypoint mapping to mark-out territory (A to B to C...) and this sequence, when brought around back to the beginning creates a sense of 'ownership', of 'mineness'.
	pages.prodigy.net /lofting/markov.html (1138 words)

	Wilmott Forums - Previsible Vs. Martingale Process
		A markov process is just a process who's expected future value depends only on the current state of the system.
		A Markov chain is first of all a DISCRETE time process, where at each discrete time point, the process can only take one out of a set of finite values.
		As regards previsibility of continuous time processes, the standard (technical) definition for a process to be previsible is that X(t) is F_t- measurable, where F_t- is the sigma algebra generated by taking the union over sigma algebras F_s where s is less than t.
	www.wilmott.com /messageview.cfm?catid=8&threadid=5019 (1392 words)

	Gauss–Markov process - Wikipedia, the free encyclopedia
		As one would expect, Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes.
		There exists a non-zero scalar function h(t) and a non-decreasing scalar function f(t) such that X(t) = h(t)W(f(t)), where W(t) is the standard Wiener process.
		Property (3) means that every Gauss–Markov process can be synthesized from the standard Wiener process (SWP).
	en.wikipedia.org /wiki/Gauss-Markov_process (162 words)

	Markov Analysis Software
		MKV is a Markov Analysis program for analysing state transition diagrams (markov chain) using numerical integration techniques.
		Markov analysis provides a means of analysing the reliability and availability of systems whose components exhibit strong dependencies.
		The major drawback of Markov methods is that Markov diagrams for large systems are generally exceedingly large and complicated and difficult to construct.
	www.isograph.com /markov.htm (623 words)

	Modeling credit risk by Richard Skora
		The Mover-Stayer process is the union of two Markov processes, and it is not a Markov process.
		A second reason why the Markov model is not accurate is that the transition from the current credit ratings to the next apparently depends on more than just the current credit rating.
		To apply this model one would have to determine a process for economic expansion and economic contraction, that is, determine when the economy is one state or the other.
	www.fenews.com /fen16/creditrisk.html (1450 words)

	Hidden Markov Models
		A discrete-time, discrete-space dynamical system governed by a Markov chain emits a sequence of observable outputs: one output (observation) for each state in a trajectory of such states.
		Now the Markov process is not hidden at all and the HMM is just a Markov chain.
		To estimate the lambda parameters for this Markov chain it is enough just to calculate the appropriate frequencies from the observed sequence of outputs.
	www.cs.brown.edu /research/ai/dynamics/tutorial/Documents/HiddenMarkovModels.html (1359 words)

	Markov Analysis Software, Markov Process & Model - Relex Software
		Markov analyses study dependent random events—events whose likelihood depends on what happened last, or where the sequence of occurrence must be considered for analysis.
		Relex Markov provides a complete set of intuitive editing tools to streamline the diagramming process, freeing you to devote more time interpreting the analyses instead of diagram construction.
		Markov modeling enables you to account for combinations of system complexities such as standby failures, non-standard common cause failures, induced failure and shared load systems, imperfect fault coverage and switch-over mechanisms, repair priorities, limited repair resources, and failure sequence dependent consequences.
	www.relex.com /products/markov.asp (691 words)

	Pinching and twisting Markov processes, Steven N. Evans, Richard B. Sowers (Site not responding. Last check: 2007-10-08)
		The state space of the new Markov process is obtained by a pinching operation that identifies points of the original state space via an equivalence relationship.
		The "Markovianity'' of the new process is ensured by suitable intertwining relationships between the semigroup of the original process and the pinching and twisting operations.
		We construct the new Markov process, identify its resolvent and transition function and, under some natural assumptions, exhibit a core for its generator.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.aop/1046294318 (423 words)

	The Fastest Mixing Markov Process on a Graph and a Connection to a Maximum Variance Unfolding Problem - Sun, Boyd, ... (Site not responding. Last check: 2007-10-08)
		Abstract: We consider a Markov process on a connected graph, with edges labeled with transition rates between the adjacent vertices.
		The distribution of the Markov process converges to the uniform distribution at a rate determinined by the second smallest eigenvalue # 2 of the Laplacian of the weighted graph.
		The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem.
	citeseer.ist.psu.edu /669286.html (635 words)

	Gauss-Markov process: Encyclopedia topic (Site not responding. Last check: 2007-10-08)
		This article is not about the Gauss-Markov theorem (Gauss-Markov theorem: more facts about this subject) of mathematical statistics (statistics: A branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters).
		There exists a non-zero scalar function h(t) and a non-decreasing scalar function f(t) such that X(t) = h(t)W(f(t)), where W(t) is the standard Wiener process (standard Wiener process: the term brownian motion (in honor of the botanist robert brown) refers to either...
		Exponential autocorrelation (autocorrelation: autocorrelation is a mathematical tool used frequently in signal processing for analysing...
	www.absoluteastronomy.com /reference/gauss-markov_process (222 words)

	Citations: An introduction to the application of the theory of probabilistic functions of a markov process to automatic ... (Site not responding. Last check: 2007-10-08)
		An introduction to the application of the theory of probabilistic functions of a markov process to automatic speech recognition.
		Levinson, L. Rabiner, and M. Sondhi, "An introduction to the application of the theory of probabilistic function of a Markov process to automatic speech processing," Bell Syst.
		In this case,the transition costs Pij are set equal to fixed penalties of H for the case i: j and V for the case i: j 2.
	citeseer.ist.psu.edu /context/40234/0 (2447 words)

	markov process - OneLook Dictionary Search
		Markov process : Glossary of research economics [home, info]
		Markov process : FOLDOP - Free On Line Dictionary Of Philosophy [home, info]
		Phrases that include markov process: continuous time markov process, gauss markov process, semi markov process, smith's markov process th, smiths markov process th
	www.onelook.com /?w=markov+process&ls=a (234 words)

	Markov Decision Process (MDP) Toolbox for Matlab
		(Notice that what the agent sees depends on what it does, which reflects the fact that perception is an active process.) The agent is also modelled as stochastic FSM with inputs (observations/rewards sent from the environment) and outputs (actions sent to the environment).
		A Markov Decision Process (MDP) is just like a Markov Chain, except the transition matrix depends on the action taken by the decision maker (agent) at each time step.
		Unfortunately, the observations are not Markov (because two different states might look the same), which invalidates all of the MDP solution techniques.
	www.cs.ubc.ca /~murphyk/Software/MDP/mdp.html (1680 words)

	Markov Decision Process Toolbox for MATLAB (Site not responding. Last check: 2007-10-08)
		Markov Decision Process (MDP) Toolbox v2.0 for MATLAB
		The MDP toolbox proposes functions related to the resolution of discrete-time Markov Decision Process : finite horizon, value iteration, policy iteration, linear programming algorithms with some variants.
		Markov Decision Processes, Martin L. Puterman, John Wiley andSons, New-York., 1994.
	www.inra.fr /bia/T/MDPtoolbox (172 words)

	markov chain - Definitions from Dictionary.com
		n : a Markov process for which the parameter is discrete time values [syn: Markov chain, Markoff chain]
		A Markov process is governed by a Markov chain.
		In simulation, the principle of the Markov chain is applied
	dictionary.reference.com /search?q=markov%20chain (108 words)

	2.5 Markov Processes (Site not responding. Last check: 2007-10-08)
		is a stochastic process that has a limited form of ``historical'' dependency [
		Eq.(2.4) states that the evolution of a Markov process at a future time, conditioned on its present and past values, depends only on its present value [
		The condition of Eq.(2.4) is also known as Markov property.
	www.cs.wm.edu /~riska/main/node13.html (86 words)

	Markov Decision Process Editor (Site not responding. Last check: 2007-10-08)
		The project is to design and implement a drawing package for Markov Processes (MPs) and Markov Decision Processes (MDPs), which we can think of as graphs with some extra information added to them.
		In the Markov Process on the left, the probability of moving from the start state (S) to state A is 0.7 while the probability of moving from S to B is 0.3.
		Knowledge of Markov Decision Processes is not required (except for some of the extensions).
	www.cs.bris.ac.uk /~kovacs/student.projects/mdp.editor.html (504 words)

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