# Markov chain

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The concept of a **Markov chain** was developed by Andrey Andreyevich Markov. A Markov chain is a sequence of random variables with the property that it is forgetful of all but its immediate past.
For a process evolving on a space and governed by an overall probability law to be a time-homogeneous Markov chain there must be a set of "transition probabilities" for appropriate sets such that
for times in (Ref. 1 Eq. 1.1)

that is denotes the probability that a chain at *x* will be in the set *A* after *n* steps, or transitions. The independence of on the values of is the Markov property,
and the independence of and *m* is the time-homogeneity property.