On the rate of convergence of Borovkov's multidimensional ergodic Markov chain

Abstract

This paper is concerned with the multidimensional Markov chain {X(n)} = {X(x, n)}, considered by Borovkov [1], [2], [3], with the form X(n + 1) = ?(n) + ?(?(n), n), where the distribution of depends only on x. Sufficient conditions on moments of |?(x)| are established for the Markov chain {X(n)} to have rate of convergence results (i.e. geometric ergodicity or sub-geometric rates for a variety of rate functions).