On Dobrushin's central limit theorem for non-homogeneous Markov chain array scheme

TL;DR

This paper introduces a new sufficient condition for the central limit theorem to hold in non-homogeneous Markov chains, even when the original Dobrushin condition does not apply.

Contribution

It proposes a novel version of Dobrushin's condition that extends the CLT applicability to broader classes of non-homogeneous Markov chains.

Findings

The new condition guarantees CLT validity where Dobrushin's original condition fails.

The approach broadens the understanding of limit theorems in non-homogeneous Markov processes.

The results are applicable to a wider range of stochastic models.

Abstract

A new version of a sufficient condition of a Dobrushin type is proposed for non-homogeneous Markov chains for a certain class of such processes. The original Dobrushin's condition may fail, yet, the CLT is still valid