On the quenched CLT for stationary Markov chains

TL;DR

This paper establishes new sufficient conditions for the quenched central limit theorem in stationary Markov chains by introducing a novel conditioning approach involving both past and future states.

Contribution

It proposes a new method of conditioning and provides fresh sufficient projective conditions for the quenched CLT in Markov chains.

Findings

New sufficient conditions for quenched CLT

A novel conditioning technique involving past and future

Applications to projective criteria for Markov chains

Abstract

In this paper we give sufficient conditions for the almost sure central limit theorem started at a point, known under the name of quenched central limit theorem. This is achieved by using a new idea of conditioning with respect to both the past and the future of the Markov chain. As applications we provide a new sufficient projective conditions for the quenched CLT.