Non-uniform Berry-Esseen theorems for weakly dependent random variables

TL;DR

This paper establishes non-uniform Berry-Esseen bounds for various weakly dependent random sequences, including Markov chains and dynamical systems, enhancing understanding of their convergence rates.

Contribution

It provides new non-uniform Berry-Esseen estimates applicable to a broad class of weakly dependent processes, extending classical results.

Findings

Derived bounds for Markov chains and dynamical systems.

Applicable to products of random matrices and local statistics.

Improved understanding of convergence rates for dependent sequences.

Abstract

We obtain non-uniform Berry-Esseen type estimates for several classes of weakly dependent sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or expanding dynamical systems, products of random matrices and some classes of local statistics.