Tuesday, October 20, 2009
10:30 AM in REC 307
Frederi Viens
Professor of Statistics and Mathematics, Purdue University

Extensions of the Nourdin-Peccati Analysis on Wiener space

Abstract

Ivan Nourdin and Giovanni Peccati have recently established results in stochastic analysis by which, for a scalar random variable X which is differentiable in the sense of Malliavin calculus (|DX| is square-integrable), an important quantity to study is the random variable G=<DX,-DMX>, where M is the pseudo-inverse of the so-called Ornstein-Uhlenbeck semigroup generator on Wiener space. For instance G is a random way of measuring the dispersion of X since Var[X]=E[G]; plus, G is constant if and only if X is Gaussian; and comparing G to a constant can yield comparisons of X to the Gaussian law, as in limit theorems or density formulas. We will review such results, their extensions to vector-valued X's, and to iterations of the map taking X to G. These are collected in papers by Airault, Malliavin, and the speaker; Nourdin and Peccati; Nourdin, Peccati, and Reveillac; Nourdin and the speaker; and a single-authored paper by the speaker.