Large deviations for sums of random variables connected into a Markov chain in approximation by Poisson law

Abstract

We consider sums of random variables (r.v.'s) connected, in each series, into a stationary Markov chain. Probabilities of large deviations of these sums in approximation by Poisson law are studied. We obtain asymptotic reD.tions for large deviations and exponential estimates for chains with uniformly strong mixing. The general case of L'-regular Markov chains is also studied.