On the local limit theorems for psi-mixing Markov chains

TL;DR

This paper studies the local limit theorem for additive functionals of nonstationary Markov chains with various moment conditions, emphasizing the role of weak dependence measured by mixing coefficients.

Contribution

It extends local limit theorem results to nonstationary Markov chains with finite or infinite second moments under weak dependence conditions.

Findings

Established local limit theorems for nonstationary Markov chains.

Identified conditions on moments and mixing coefficients for the theorems.

Provided new insights into the dependence structure affecting limit behaviors.

Abstract

In this paper we investigate the local limit theorem for additive functionals of a nonstationary Markov chain with finite or infinite second moment. The moment conditions are imposed on the individual summands and the weak dependence structure is expressed in terms of some uniformly mixing coefficients.