David Nualart

Malliavin Calculus and Normal Approximations

University of Kansas

The purpose of this talk is to make an heuristic introduction to the stochastic calculus of variations, that was introduced by Paul Malliavin in the 70’s in order to provide a probabilistic proof of Hörmander’s hypoellipticity theorem. We will discuss the application Malliavin calculus, combined with Stein’s method for normal approximations, to establish upper bounds for total variation distances in the context of central limit theorems. This methodology will be illustrated by two examples: central limit theorems for stationary sequences and asymptotic behavior of spatial averages of the stochastic heat equation.

Friday, November 3, 14h30