In this paper, sufficient conditions are given for the existence of limiting distribution of a nonho-mogeneous countable Markov chain with time-dependent transition intensity matrix. The method of proof exploits the fact that if the distribution of random process Q = (Qtt≥0 (is absolutely continuous with)respect to the distribution of ergodic random process Qo = (Qtot≥0, then (Formula presented), where π is the invariant measure of Qo. We apply this result for asymptotic analysis, as t → ∞, of a nonhomogeneous countable Markov chain which shares limiting distribution with an ergodic birth-and-death process.
Queueing Systems, Vol. 46, no. 3-4 (Mar 2004), pp. 353-361