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

Diego F. de Bernardini; Christophe Gallesco; Serguei Popov

doi:10.1016/j.spa.2017.10.015

paper

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

arXiv:1610.02532 · doi:10.1016/j.spa.2017.10.015

Abstract

In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of $n$ i.i.d. random variables with law given by the invariant measure of that Markov chain. The proof of this result uses a refinement of the soft local time method of [11].

42 pages, 2 figures, coupling construction of Section 4 corrected, results unchanged