A Useful Version of the Central Limit Theorem for a General Class of Markov Chains

TL;DR

This paper introduces verifiable conditions that guarantee the central limit theorem for a broad class of Markov chains, with applications to modeling stochastic gene expression in prokaryotes.

Contribution

It proposes a practical criterion for the CLT in Markov chains and demonstrates its application to a biological system, enhancing analysis of stochastic dynamics.

Findings

Established verifiable conditions for CLT in Markov chains

Applied the criterion to a biological Markov system

Provided insights into stochastic gene expression

Abstract

In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of our criterion, we further verify it for a particular discrete-time Markov dynamical system. From the application point of view, the examined system provides a useful tool in analysing the stochastic dynamics of gene expression in prokaryotes.