Central limit theorem for triangular arrays of Non-Homogeneous Markov chains

Abstract

In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower bound estimate for the variance of partial sums. The results complement an important central limit theorem of Dobrushin based on the contraction coefficient.

19 pages, submitted 2010 To appear in Probability Theory and Related Fields