UNIFORM CLT FOR MARKOV CHAINS WITH A COUNTABLE STATE SPACE

Abstract

We prove a uniform CLT for Markov chains for functions dominated by a function in a $L^{2}$-space. Using empirical process CLT's for stationary sequences satisfying a variety of mixing conditions one can obtain similar results. However, our conditions are less restrictive than those required for a mixing process application to these problems, and an example is given to these differences.