Local limit theorems for inhomogeneous Markov chains

TL;DR

This paper establishes local limit theorems for inhomogeneous Markov chains and applies these results to derive precise large deviation asymptotics, advancing understanding of their probabilistic behavior.

Contribution

It introduces new reduction theorems for Markov arrays and proves local limit theorems for bounded additive functionals of inhomogeneous Markov chains.

Findings

Proved local limit theorems for inhomogeneous Markov arrays.

Derived precise large deviation asymptotics for Markov chains.

Developed new reduction theorems for Markov arrays.

Abstract

We prove the Local Limit Theorems for bounded additive functionals of uniformly elliptic inhomogeneous Markov arrays. As an application we obtain the precise asymptotics in the large deviation regime for bounded additive functionals of uniformly elliptic Markov chains. The proofs rely on new reduction theorems for Markov arrays.