Central limit theorems for sums of α-mixing random variables

Abstract

In this paper we prove central limit theorems for sums of random variables belonging to a triangular array. We assume that this array satisfies the α-mixing property. One central limit theorem stales me convergence in distribution without any assumption on the finiteness of moments. Finally, we apply one of the central limit theorems proved before to the problem of estimating the stationary density of a Markov chain.