Central limit theorem for triangular arrays of Non-Homogeneous Markov chains

TL;DR

This paper establishes a central limit theorem for non-homogeneous Markov chains arranged in triangular arrays, using martingale methods and correlation bounds, extending previous results by Dobrushin.

Contribution

It introduces a new CLT for non-homogeneous Markov chains under correlation constraints, complementing Dobrushin's theorem with novel techniques.

Findings

Proves CLT for triangular arrays of non-homogeneous Markov chains.

Uses martingale techniques and variance bounds in the proof.

Extends the scope of existing CLT results for Markov processes.

Abstract

In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower bound estimate for the variance of partial sums. The results complement an important central limit theorem of Dobrushin based on the contraction coefficient.