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In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process. It is named after the Russian mathematician Andrey Markov.〔Markov, A. A. (1954). ''Theory of Algorithms''. (by Jacques J. Schorr-Kon and PST staff ) Imprint Moscow, Academy of Sciences of the USSR, 1954 (Israel Program for Scientific Translations, 1961; available from Office of Technical Services, United States Department of Commerce ) Added t.p. in Russian Translation of Works of the Mathematical Institute, Academy of Sciences of the USSR, v. 42. Original title: ''Teoriya algorifmov''. (Dartmouth College library. U.S. Dept. of Commerce, Office of Technical Services, number OTS 60-51085. )〕 A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present states) depends only upon the present state, not on the sequence of events that preceded it. A process with this property is called a ''Markov process''. 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. Both the terms "Markov property" and "strong Markov property" have been used in connection with a particular "memoryless" property of the exponential distribution.〔Feller, W. (1971) ''Introduction to Probability Theory and Its Applications, Vol II'' (2nd edition),Wiley. ISBN 0-471-25709-5 (pages 9 and 20)〕 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〔Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'' OUP. ISBN 0-19-850994-4〕 extends this property to two or more dimensions or to random variables defined for an interconnected network of items. 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. ==Introduction== A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present values) depends only upon the present state; that is, given the present, the future does not depend on the past. A process with this property is said to be Markovian or a Markov process. The most famous Markov process is a Markov chain. Brownian motion is another well-known Markov process. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Markov property」の詳細全文を読む スポンサード リンク
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