Convergence rates for discrete-time Markov chains in total variation distance

Abstract

In this paper, we study convergence rates for ergodic discrete-time Markov chians in total variation distance. When the initial distribution of a Markov chain satis es some integrability conditions, convergence rates are estimated by using Poincare, weak Poincare, log-Sobolev and weak log-Sobolev inequalities. Moreover, integrability conditions of the initial distribution are weakened by a truncation method.