The purpose of this talk is to provide a heuristic introduction to the stochastic calculus of variations, introduced by Paul Malliavin in the 1970s to offer a probabilistic proof of Hörmander's hypoellipticity theorem. We will discuss the application of 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 through two examples: central limit theorems for stationary sequences and the asymptotic behavior of spatial averages of the stochastic heat equation.
Friday, November 3, 14:30