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

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.

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."