Berry-Esseen bounds in local limit theorems

TL;DR

This paper develops Berry-Esseen bounds for the multidimensional local limit theorem, providing explicit error estimates based on Lyapunov coefficients and density maxima.

Contribution

It introduces new bounds in the local limit theorem that improve understanding of convergence rates in multidimensional settings.

Findings

Bounds expressed in terms of Lyapunov coefficients

Bounds depend on maxima of involved densities

Enhanced error estimates for multidimensional distributions

Abstract

Berry-Esseen-type bounds are developed in the multidimensional local limit theorem in terms of the Lyapunov coefficients and maxima of involved densities.