A new criterion for recurrence of Markov chains with an infinitely countable set of states

Vyacheslav M. Abramov

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arXiv · 2402.16004

A new criterion for recurrence of Markov chains with an infinitely countable set of states

Vyacheslav M. Abramov

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Abstract

For a class of irreducible Markov chains with an infinitely countable set of states, we establish a new verifiable necessary and sufficient condition for recurrence and transience. We show that if one of the basic assumptions is not satisfied, then the statement of the theorem becomes invalid.

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Vyacheslav M. Abramov. 2024-02-25. A new criterion for recurrence of Markov chains with an infinitely countable set of states. https://arxiv.org/abs/2402.16004

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