Multivariate normal approximation using Stein's method and Malliavin calculus

Abstract

We combine Stein's method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Among several examples, we provide an application to a functional version of the Breuer-Major CLT for fields subordinated to a fractional Brownian motion. © Association des Publications de l'Institut Henri Poincaré, 2010.