On uniform closeness of local times of Markov chains and i.i.d. sequences

Diego F. de Bernardini, Christophe Gallesco, Serguei Popov

Published 2016-10-08Version 1

In this paper we use the soft local time technique to obtain a coupling between the field of local times at time $n$ of a Markov chain, and the one of a sequence of $n$ i.i.d. random variables with law given by the invariant measure of that Markov chain. As a result, we obtain upper bounds on the total variation distance between the two fields, which are uniform in $n$.