Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes

Abstract

We derive the conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results by Menshikov and Volkov [Electron. J. Probab., 13 (2008), paper No. 31, 944--960] follow.

arXiv commentMinor corrections are made. The paper is accepted for publication in "Bulletin of the Australian Mathematical Society"