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arXiv 2402.160042024-02math.PR

状态集为可数无限集的马尔可夫链常返性的一个新判据

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

Vyacheslav M. Abramov

备注：: 15 pages in the journal format. Initial title is changed. This is a substation revision and the final version that is accepted for publication in "Theory of Probability and Mathematical Statistics."

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AI总结：

本研究针对可数无限状态集的不可约马尔可夫链，提出了新的可验证常返性与非常返性充要条件，并验证了基本假设不满足时定理结论失效。

摘要：

针对一类状态集为可数无限集的不可约马尔可夫链，我们建立了一个新的可验证的常返性与非常返性充要条件。我们证明，若其中一个基本假设不满足，则该定理的结论不成立。

英文摘要：

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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