Markov chain, generalized

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2010 Mathematics Subject Classification: Primary: 60J10 [MSN][ZBL]

A sequence of random variables with the properties:

1) the set of values of each is finite or countable;

2) for any and any ,


A generalized Markov chain satisfying (*) is called -generalized. For , (*) is the usual Markov property. The study of -generalized Markov chains can be reduced to the study of ordinary Markov chains. Consider the sequence of random variables whose values are in one-to-one correspondence with the values of the vector

The sequence forms an ordinary Markov chain.


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How to Cite This Entry:
Markov chain, generalized. Encyclopedia of Mathematics. URL:,_generalized&oldid=26566
This article was adapted from an original article by V.P. Chistyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article