On the CLT for stationary Markov chains with trivial tail sigma field

TL;DR

This paper proves a central limit theorem for additive functionals of stationary Markov chains with trivial tail sigma fields, under the condition that the variance of partial sums grows at most linearly.

Contribution

It establishes the CLT for this class of Markov chains under a variance boundedness condition, extending previous results.

Findings

CLT holds for additive functionals of stationary Markov chains with trivial tail sigma fields.

Variance of partial sums divided by n remains bounded in the studied setting.

Provides theoretical conditions ensuring normal convergence of partial sums.

Abstract

In this paper we consider stationary Markov chains with trivial two-sided tail sigma field, and prove that additive functionals satisfy the central limit theorem provided the variance of partial sums divided by n is bounded.