Stein’s method for Markov chains: first examples

Abstract

Charles Stein has introduced a general approach to proving approximation theorems in probability theory. The method is being actively used for normal and Poisson approximation. This paper uses the method to derive rates of convergence of some simple Markov chains to their stationary distribution. The main purpose is to present Stein’s general approach in a simple setting where the many choices can be examined and compared.