Non-uniform Berry-Esseen bounds via Malliavin-Stein method

TL;DR

This paper develops non-uniform Berry-Esseen bounds using the Malliavin-Stein method, with applications to Wiener-Itô integrals and Brownian motion functionals, advancing probabilistic approximation techniques.

Contribution

It introduces a novel approach to non-uniform Berry-Esseen bounds leveraging the Malliavin-Stein method, with specific applications to stochastic integrals and Brownian motion.

Findings

Established new non-uniform Berry-Esseen bounds

Applied bounds to Wiener-Itô integrals and Brownian motion functionals

Enhanced understanding of probabilistic approximation accuracy

Abstract

In this paper, we establish non-uniform Berry-Esseen bounds by means of the Malliavin-Stein method. Applications to the multiple Wiener-It\^o integrals and the exponential functionals of Brownian motion are given to illustrate the theory.