Markov process

Markov process
a process in which future values of a random variable are statistically determined by present events and dependent only on the event immediately preceding.
Also, Markoff process.
[1935-40; after Russian mathematician Andrei Andreevich Markov (1856-1922), who developed it]

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sequence of possibly dependent random variables (x1, x2, x3, …)—identified by increasing values of a parameter, commonly time—with the property that any prediction of the next value of the sequence (xn), knowing the preceding states (x1, x2, …, xn − 1), may be based on the last state (xn − 1) alone. That is, the future value of such a variable is independent of its past history.

These sequences are named for the Russian mathematician Andrey Andreyevich Markov (Markov, Andrey Andreyevich) (1856–1922), who was the first to study them systematically. Sometimes the term Markov process is restricted to sequences in which the random variables can assume continuous values, and analogous sequences of discrete-valued variables are called Markov chains. See also stochastic process.

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Universalium. 2010.

Look at other dictionaries:

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• Markov process — In probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time varying random phenomenon for which a specific property (the Markov property) holds. In a common description, a stochastic… …   Wikipedia

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