Moderate deviations for empirical measures for nonhomogeneous Markov chains

TL;DR

This paper establishes moderate deviation principles for empirical measures of countable nonhomogeneous Markov chains, assuming uniform Cesàro convergence of their transition probabilities.

Contribution

It introduces a new moderate deviation result for empirical measures under Cesàro convergence conditions for nonhomogeneous Markov chains.

Findings

Moderate deviations hold under Cesàro convergence.

Results apply to countable nonhomogeneous Markov chains.

Provides theoretical foundation for empirical measure analysis.

Abstract

We prove that moderate deviations for empirical measures for countable nonhomogeneous Markov chains hold under the assumption of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chains in Ces\`aro sense.