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

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.

The new version of the manuscript is focused on the central limit theorem only. The proofs are now more precise. The part concerning the law of the iterated logarithm is postponed to the subsequent paper. Splitting the article into two papers is certainly for the benefit of the reader, since even this single part consists of 25 pages