Approximation of the density of a solution of a nonlinear SDE — application to parabolic SPDEs

Abstract

This paper studies the approximation of the density P t, x ( y) of the solution of the nonlinear limit-problem of a system of weakly interacting SDE's via a convolution of the empirical measure of the system with a family of smooth mollifiers. The method, which mainly uses coupling techniques and Malliavin calculus, is also applied to the case of nonlinear white-noise driven parabolic SPDEs.