Lindeberg theorem for Gibbs–Markov dynamics

Abstract

A dynamical array consists of a family of functions and a family of initial times . For a dynamical system we identify distributional limits for sums of the formfor suitable (non-random) constants and . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs–Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs–Markov dynamical systems for convenience.