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.
Keywords
Cite
@article{arxiv.1804.09220,
title = {A Useful Version of the Central Limit Theorem for a General Class of Markov Chains},
author = {Dawid Czapla and Katarzyna Horbacz and Hanna Wojewódka-Ściążko},
journal= {arXiv preprint arXiv:1804.09220},
year = {2020}
}
Comments
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