On the local limit theorems for lower psi-mixing Markov chains

TL;DR

This paper establishes local limit theorems for additive functionals of nonstationary Markov chains with lower psi-mixing conditions, extending results to both lattice and non-lattice cases and connecting to stable distribution convergence.

Contribution

It introduces new local limit theorems for nonstationary Markov chains under lower psi-mixing conditions, applicable to both lattice and non-lattice scenarios, including stationary cases.

Findings

Local limit theorems for nonstationary Markov chains

Results applicable to lattice and non-lattice cases

Extension to convergence to stable distributions

Abstract

In this paper we investigate the local limit theorem for additive functionals of nonstationary Markov chains that converge in distribution. We consider both the lattice and the non-lattice cases. The results are also new in the stationary setting and lead to local limit theorems linked to convergence to stable distributions. The conditions are imposed to individual summands and are expressed in terms of lower psi-mixing coefficients.