Berry-Esseen estimates for regenerative processes under weak moment assumptions

TL;DR

This paper establishes Berry-Esseen bounds for the convergence rates in CLTs of regenerative processes under weaker moment conditions, extending previous results and applying to Markov chains and random walks.

Contribution

It generalizes Berry-Esseen estimates for regenerative processes by weakening moment assumptions and applies these results to Markov chains and random walks in random environments.

Findings

Established Berry-Esseen rates under weaker moment conditions.

Applied results to CLTs for Markov chains with strong mixing.

Extended CLT convergence rates to ballistic random walks.

Abstract

We prove Berry-Esseen type rates of convergence for central limit theorems (CLTs) of regenerative processes which generalize previous results of Bolthausen under weaker moment assumptions. We then show how this general result can be applied to obtain rates of convergence for (1) CLTs for additive functionals of positive recurrent Markov chains under certain conditions on the strong mixing coefficients, and (2) annealed CLTs for certain ballistic random walks in random environments.