Stein's method and normal approximation of poisson functionals

Abstract

We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Esséen bounds in Central limit theorems (CLTs) involving multipleWiener-Itô integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck Lévy processes.