Subgeometric ergodicity of Markov chains

TL;DR

This paper provides a concise, self-contained proof of subgeometric convergence rates for Markov chains using coupling and a general drift condition, enhancing understanding and practical application of convergence bounds.

Contribution

It offers a simplified, intuitive proof of subgeometric ergodicity bounds based on coupling and a broad drift condition, extending prior theoretical results.

Findings

Provides practical bounds for subgeometric convergence rates.

Uses coupling method for intuitive understanding.

Employs a general drift condition for broad applicability.

Abstract

The goal of this paper is to give a short and self contained proof of general bounds for subgeometric rates of convergence, under practical conditions. The main result whose proof, based on coupling, provides an intuitive understanding of the results of Nummelin and Tuominen (1983) and Tuominen and Tweedie (1994). To obtain practical rates, a very general drift condition, recently introduced in Douc et al (2004) is used.