A Remark on a Large Deviation Theorem for Markov Chain with a Finite Number of States

Abstract

We consider the classic problem of large deviations for sums of random variables defined on the states of homogeneous Markov chain with finite phase space. The exact asymptotics for probabilities of large deviations of order $O(\sqrt n)$ is established. The proof is based on application of a local theorem of a new type.