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Topic: Markov property

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	Markov property - Wikipedia, the free encyclopedia
		In probability theory, a stochastic process has the Markov property if the conditional probability distribution of future states of the process, given the present state and all past states, depends only upon the current state and not on any past states, i.e.
		A process with the Markov property is usually called a Markov process, and may be described as Markovian.
		The most famous Markov processes are Markov chains, but many other processes, including Brownian motion, are Markovian.
	en.wikipedia.org /wiki/Markov_property (258 words)

	Encyclopedia :: encyclopedia : Property (philosophy) (Site not responding. Last check: 2007-11-05)
		In philosophy, mathematics, and logic, a property is an attribute of an object; thus a red object is said to have the property of redness.
		Properties are therefore subject to the Russell's paradox/Grelling-Nelson paradox.
		It differs from the logical concept of class by not having any concept of extensionality, and from the philosophical concept of class in that a property is considered to be distinct from the objects which possess it.
	www.hallencyclopedia.com /Property_(philosophy) (167 words)

	[No title]
		Markov graduated from St. Petersburg University in 1878, and at the age of 30, he became a professor of the same university and a member of the St. Petersburg Academy of Sciences.
		Markov’s work in this area was mainly motivated by his efforts to extend the laws of large numbers and central limit theorem to dependent sequences, which was believed to be an impossible goal the time.
		It is fitting that these mathematical objects bear Markov’s name, acknowledging his trailblazing role in the development of processes that exhibit the Markov property.
	appliedprob.society.informs.org /APS_Markov_bio.doc (286 words)

	Markov property - Wikipédia
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		Sacara informal, prosés stokastik mibanda sipat Markov if the conditional probability distribution of future states of the process, given the present state, depends only upon the current state, and conditionally independent of the past states (the path of the process) given the present state.
		Prosés Markov nu pangkawentarna nyaéta ranté Markov, ngan prosés-prosés séjénna ogé, kaasup gerak Brown (Ing.
	su.wikipedia.org /wiki/Markov_property (252 words)

	[No title]
		Because data may merely approach a Markov process, a quantitative assessment of the closeness of that approach was devised from the concept of uncertainty (entropy) developed by Claude Shannon in his mathematical theory of communication.
		A common way to illustrate Markov chain dependencies is to construct a "box and arrow" diagram, where the boxes represent the kinds of events and the arrows represent first-order transitions from one event to the next.
		Markov chains cannot handle this problem logically, but the user can focus upon switches in behavior to code a succession of events that will usually reveal important aspects of how one animal's behavior is influencing that of the other.
	www.animalbehavior.org /Resources/CSASAB/uncert.doc (2356 words)

	Introduction
		Markov processes, named for Andrei Markov are among the most important of all random processes.
		For a Markov chain, the ordinary Markov property implies the strong Markov property.
		The study of Markov chains is simplified by the use of operator notation that is analogous to operations on vectors and matrices.
	www.math.uah.edu /stat/markov/Introduction.xhtml (1043 words)

	Markov chain - MLpedia
		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.
		The world's mobile telephone systems depend on the Viterbi algorithm for error-correction, while Hidden Markov models (where the Markov transition probabilities are initially unknown and must also be estimated from the data) are extensively used in speech recognition and also in bioinformatics, for instance for coding region/gene prediction.
		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.
	www.mlpedia.org /index.php?title=Markov_chain (1498 words)

	SCOPE 34 - Practitioner's Handbook on the Modelling of Dynamic Change in Ecosystems, Chapter 6, Markov Models and ... (Site not responding. Last check: 2007-11-05)
		A Russian mathematician, Markov, who lived early in the 20th century defined one such class of processes, in which the probability of the process being in a given state at a particular time is related to the immediately preceding state of that process.
		A Markov chain is, therefore, a sequence or chain of discrete states in time or space with fixed probabilities for the transition from one state to a given state in the next step in the chain.
		In the Markov model a random component is present, so that the state of the system at any point of time or space is not wholly dependent on the previous event or events, but there is, nevertheless, a structure of successive events which defines the process.
	www.icsu-scope.org /downloadpubs/scope34/chapter6.html (6220 words)

	Markov Chains
		A Markov chain, named in honor of Russian mathematician Andrei Markov, is a stochastic process.
		Markov chain is said to be irreducible, if there is only one class, that is, all states
		Markov chains also have many biological applications, particularly population processes, which are useful in modelling processes that are, at least, analogous to biological populations.
	cs.bilgi.edu.tr /~bulent/MarkovChains.html (1400 words)

	Markov Model
		The name Markov model is derived from one of the assumptions which allows this system to be analyzed; namely the Markov property.
		The Markov property states: given the current state of the system, the future evolution of the system is independent of its history.
		Markov models are applicable to systems with common cause failures, such as an electrical lightning storm shock to a computer system.
	www.markov-model.com (557 words)

	3.5 The Markov Property
		In particular, we formally define a property of environments and their state signals that is of particular interest, called the Markov property.
		This is sometimes also referred to as an "independence of path" property because all that matters is in the current state signal; its meaning is independent of the "path," or history, of signals that have led up to it.
		The Markov property is important in reinforcement learning because decisions and values are assumed to be a function only of the current state.
	www.cs.ualberta.ca /~sutton/book/ebook/node32.html (2071 words)

	State function (Site not responding. Last check: 2007-11-05)
		In thermodynamics, a state function is any property of a system that depends only on the current state of the system, not on the way in which the system got to that state.
		It is best to think of state functions as quantities or properties of a thermodynamic system, while non-state functions represent a process during which the state functions change.
		For example, the state function PV is proportional to the internal energy of an ideal gas, but the work W is the amount of energy transferred as the system performs work.
	www.brainyencyclopedia.com /encyclopedia/s/st/state_function.html (603 words)

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	Markov chains
		A Markov chain is a discrete stochastic process with discrete states and discrete transformations between them.
		This is called the Markov property of the chain.
		Because of the Markov property, the complete probability distribution of the states of a Markov chain is defined by the initial distribution
	www.cis.hut.fi /ahonkela/dippa/node33.html (156 words)

	Markov Chains
		The construction of a Markov chain requires two basic ingredients, namely a transition matrix and an initial distribution.
		The first identity in (2.3), which is also called ``Markov property'', defines the ``memory'' or ``order'' of the chain.
		Although aperiodicity may be omitted, we will have this property in the examples discussed in Chapter 3.
	random.mat.sbg.ac.at /~ste/diss/node6.html (979 words)

	Transwiki:Markovian - Wiktionary
		In probability theory, a stochastic process is said to be Markovian if it has the Markov property.
		Such a process is called a Markov process.
		An important type of Markov process is the Markov chain.
	en.wiktionary.org /wiki/Transwiki:Markovian (52 words)

	Markov Chains (Site not responding. Last check: 2007-11-05)
		A Markov chain is a special case of a Markov process, which itself is a special case of a random or stochastic process.
		A Markov chain is a discrete-state random process in which the evolution of the state of the process beginning at a time t (continuous-time chain) or n (discrete-time chain) depends only on the current state X(t) or X
		Hence, the only continuous-time, memory-less distribution is the exponential distribution, and the time between state changes in a continuous-time Markov chain is exponentially distributed.
	cnx.org /content/m10861/latest (627 words)

	Markov Chains in discrete time
		The Markov property is about independence, specifically about the future development of a process being independent of anything that has happened in the past, given its present value.
		The transition matrices of periodic Markov chains have eigenvalues on the unit circle.
		We need to decide in advance whether the situation being modelled is suited to a Markov model and whether the model should be time-homogeneous.
	www.staff.city.ac.uk /r.j.gerrard/courses/2dsm/dsm03_4.htm (1176 words)

	Mathenomicon.net : Markov property (Site not responding. Last check: 2007-11-05)
		There is at least one finitely presented semigroup with property
		There is at least one finitely presented semigroup that is `inherently bad' with regard to
		is a Markov property, then it is undecidable whether a finitely presented semigroup has property
	www.cenius.net /refer/articles/m/markovproperty/markovproperty.html (89 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		y) A Markov specification is one where each p_A(x.) is measurable in B_{b(A)} where b(A) consists of all s in S\A which have neighbours in A (i.e.
		It follows directly from the definitions that a Gibbs distribution for a Markov specification has the Markov property P(E
		If this is the case for infinite A as well, we say that P has the global Markov property.
	www.math.niu.edu /~rusin/known-math/00_incoming/markov_spec (191 words)

	Réunion d'hiver 2000 de la SMC
		A set-Markov process becomes Markov in the classical sense when it is transported by a ``flow''.
		This, for turn, is an essential step in computing such invariants of dynamical properties of a map as Conley index or Lefschetz number.
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	www.cms.math.ca /Events/winter00/abs/CP-f.html (1855 words)

	2.5 Markov Processes (Site not responding. Last check: 2007-11-05)
		This stochastic process is a Markov process if it satisfies
		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)

	Evaluating the Markov Property in Studies of Economic Convergence -- Bickenbach and Bode 26 (3): 363 -- International ...
		Evaluating the Markov Property in Studies of Economic Convergence -- Bickenbach and Bode 26 (3): 363 -- International Regional Science Review
		Evaluating the Markov Property in Studies of Economic Convergence
		To examine the reliability of estimated Markov transition
	irx.sagepub.com /cgi/content/abstract/26/3/363 (220 words)

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	www.sunnybulgarianproperties.com /propertydetailseng.aspx?id=198 (440 words)

	Table of contents for Library of Congress control number 2004048547
		Strong Markov Property and Right Continuity of Fields 56 Exercises 65 2.4.
		Moderate Markov Property and Quasi Left Continuity 66 Exercises 73 Notes on Chapter 2 73 Chapter 3 Hunt Process 75 3.1.
		Preliminary Properties of Brownian Motion 144 Exercises 152 4.3.
	www.loc.gov /catdir/toc/fy0604/2004048547.html (188 words)

	[No title]
		Foundational concepts Stationary process; weak stationarity; Markov property; Some elementary examples White noise; random walk; moving average (MA).
		¢ çÿ"çÿ"çÿ"çÿ"çÿ"çÿ" çÿ"çÿ"ª. ó@¬¨Markov Processesª ¨þDefinition: A stochastic process that has the Markov property is known as a Markov process.
		When state space is discrete but time is continuous then known as Markov jump process.
	www.ucd.ie /statdept/shanewhelan/intromod/05lectinro5-6.ppt (491 words)

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