A useful version of the central limit theorem for a general class of Markov chains

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.