When is a Markov chain regenerative?

A sequence of random variables {Xn}n≥0 is called regenerative if it can be broken up into iid components. The problem addressed in this paper is that of determining under what conditions a Markov chain is regenerative. It is shown that an irreducible Markov chain with a countable state space is rege...

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Bibliographic Details
Published in:Statistics & probability letters 2014-01, Vol.84, p.22-26
Main Authors: Athreya, Krishna B., Roy, Vivekananda
Format: Article
Language:English
Subjects:
Harris recurrence
Markov chains
Monte Carlo
Recurrence
Regenerative sequence
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Summary:A sequence of random variables {Xn}n≥0 is called regenerative if it can be broken up into iid components. The problem addressed in this paper is that of determining under what conditions a Markov chain is regenerative. It is shown that an irreducible Markov chain with a countable state space is regenerative for any initial distribution if and only if it is recurrent (null or positive). An extension of this to the general state space case is also discussed.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2013.09.021