Renewal approximation for the absorption time of a decreasing Markov Chain

Alsmeyer G., Marynych A.

Abstract

We consider a Markov chain (Mn)n>0 on the set N0 of nonnegative integers which is eventually decreasing, i.e. P{Mn+1 < Mn | Mn ≥ a} = 1 for some a ϵ N and all n ≥ 0. We are interested in the asymptotic behavior of the law of the stopping time T = T (a) := inf{k ϵ N0 : Mk