Stein's method and normal approximation of Poisson functionals

TL;DR

This paper combines Stein's method with Malliavin calculus on the Poisson space to derive explicit bounds for normal approximations in CLTs involving Poisson functionals, with applications to Ornstein-Uhlenbeck Lévy processes.

Contribution

It introduces a novel combination of Stein's method and Malliavin calculus for Poisson functionals, providing explicit Berry-Esséen bounds in CLTs.

Findings

Derived explicit Berry-Esséen bounds for Poisson functionals in CLTs.

Applied the method to Ornstein-Uhlenbeck Lévy processes.

Enhanced understanding of normal approximation in Poisson-based stochastic processes.

Abstract

We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Ess\'een bounds in Central Limit Theorems (CLTs) involving multiple Wiener-It\^o integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck L\'evy processes.