Central Limit Theorem and Moderate deviation for nonhomogenenous Markov chains

TL;DR

This paper proves a central limit theorem and a moderate deviation theorem for countable nonhomogeneous Markov chains under uniform convergence conditions, extending classical probabilistic results to more general Markov processes.

Contribution

It introduces new CLT and moderate deviation results for countable nonhomogeneous Markov chains under Cesàro convergence of transition matrices.

Findings

Established CLT for nonhomogeneous Markov chains.

Derived moderate deviation principles using Gärtner-Ellis theorem.

Extended classical results to countable state spaces.

Abstract

Our purpose is to prove central limit theorem for countable nonhomogeneous Markov chain under the condition of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chain in Ces\`aro sense. Furthermore, we obtain a corresponding moderate deviation theorem for countable nonhomogeneous Markov chain by G\"artner-Ellis theorem and exponential equivalent method.