Markov chain, generalized

2020 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.

References

[D]	J.L. Doob, "Stochastic processes" , Wiley (1953) MR1570654 MR0058896 Zbl 0053.26802

References

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[KS]	J.G. Kemeny, J.L. Snell, "Finite Markov chains" , v. Nostrand (1960) MR1531032 MR0115196 Zbl 0089.13704
[Re]	D. Revuz, "Markov chains" , North-Holland (1975) MR0415773 Zbl 0332.60045
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