On existence of limiting distribution for time-nonhomogeneous countable Markov process
In this paper, sufficient conditions are given for the existence of limiting distribution of a nonhomogeneous countable Markov chain with time-dependent transition intensity matrix. The method of proof exploits the fact that if the distribution of random process Q = (Q(t))(tgreater than or equal to0) is absolutely continuous with respect to the distribution of ergodic random process Qdegrees = (Q(t)degrees)(tgreater than or equal to0), then Q(t) -->(law)(t-->infinity)pi, where pi is the invariant measure of Qdegrees. We apply this result for asymptotic analysis, as t --> infinity, of a nonhomogeneous countable Markov chain which shares limiting distribution with an ergodic birth-and-death process.
countable markov process birth-and-death process existence of the limiting distribution