Let (F n) be any sequence of Wiener chaoses of any fixed
order converging in distribution towards a standard Gaussian. In this talk, without any
additional assumptions, we shall explain how to derive the asymptotic smoothness of
the densities of F n , as well as the convergence of all its derivatives in every L q (R) for all q ∈
[1, +∞] towards
the corresponding derivatives of the Gaussian density. In
particular, these findings
greatly improve the currently known types of convergence which are total
variation
and entropy that were obtained through Malliavin/Stein method.
Joint work with Ronan Herry and Dominique Malicet