On some Limit Theorem for Markov Chain

TL;DR

This paper establishes conditions under which a central limit theorem holds for random variables governed by hidden Markov chains, specifically when the chain is ergodic and Lindeberg's condition is satisfied.

Contribution

It provides a proof that the CLT applies to hidden Markov chain-driven variables under ergodicity and Lindeberg's condition, extending existing results.

Findings

CLT holds for ergodic hidden Markov chains with Lindeberg's condition

Conditions identified that guarantee normal convergence of sums

Theoretical proof of CLT in this context

Abstract

The goal of this paper is to describe conditions which guarantee a central limit theorem for random variables, which distributions are controled by hidden Markov chains. We proved that when a Markov chain is ergodic and random variables fullfiled Lindeberg's condition then the Central Limit Theorem is true.