On estimates of the rate of convergence In the global limit theorems for Homogeneous markov chains

Abstract

In this paper some estimates are obtained for the remainder term in the limit theorems for the weighted sum of random variables forming a homogeneous Markov chain with arbitrary set of possible states . The achieved results make it possible to estimate the rate of convergence in these theorems in the metric of the space Lp, 1 <p < °° without requiring that the absolute third order moment for the transition probabilities be bounded.