A Central Limit Theorem for Functionals of Gaussian Processes

Abstract

The aim of this thesis is to study and show, as described in the works of Nualart, that a sequence of functionals of Gaussian processes that belongs to a Wiener chaos of fixed order converges in distribution to a standard normal law. First, we will prove this in the finite-dimensional case and then extend this to the infinite-dimensional case. As an example, we will illustrate the classical Central Limit Theorem. We will also show how to apply our result to Gaussian Moving Averages.