Criteria for rates of convergence of Markov chains, with application to queueing and storage theory

Abstract

This paper first presents a review of the connections between various rate of convergence results for Markov chains (including normal Harris ergodicity, geometric ergodicity and sub-geometric rates for a variety of rate functions ψ), and finiteness of appropriate moments of hitting times on small sets. We then present a series of criteria, analogous to Foster's criterion for ergodicity, which imply the finiteness of these moments and hence the rate of convergence of the Markov chain.