CONDITIONS FOR RECURRENCE AND TRANSIENCE FOR TIME-INHOMOGENEOUS BIRTH-AND-DEATH PROCESSES

Abstract

Abstract We derive 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 [‘Urn-related random walk with drift $\rho x^\alpha /t^\beta $ ’, Electron. J. Probab.13 (2008), 944–960] follow.