Editing Markov property (section)

{{Short description|Memoryless property of a stochastic process}}
{{about|the property of a stochastic process|the class of properties of a finitely presented group|Adian–Rabin theorem}}
[[File:Wiener process 3d.png|thumb|A single realisation of three-dimensional [[Brownian motion]] for times 0 ≤ t ≤ 2. Brownian motion has the Markov property, as the displacement of the particle does not depend on its past displacements.]]

In [[probability theory]] and [[statistics]], the term '''Markov property''' refers to the [[memoryless]] property of a [[stochastic process]], which means that its future evolution is independent of its history. It is named after the [[Russia]]n [[mathematician]]  [[Andrey Markov]]. The term '''strong Markov property''' is similar to the Markov property, except that the meaning of "present" is defined in terms of a random variable known as a [[stopping time]].

The term '''Markov assumption''' is used to describe a model where the Markov property is assumed to hold, such as a [[hidden Markov model]].

A [[Markov random field]] extends this property to two or more dimensions or to random variables defined for an interconnected network of items.<ref>[[Yadolah Dodge|Dodge, Yadolah]]. (2006) ''The Oxford Dictionary of Statistical Terms'', [[Oxford University Press]]. {{isbn|0-19-850994-4}}</ref> An example of a model for such a field is the [[Ising model]].

A discrete-time stochastic process satisfying the Markov property is known as a [[Markov chain]].