Regularity of Conditional Laws in Non-Linear Filtering Theory and Stochastic Calculus of Variations

Abstract

Using the theory of stochastic partial differential equations, Krylov-Rozovskii and Pardoux obtained regularity results for conditional laws arising in non-linear filtering theory. One gives here, in a more general setting, a new method for getting that sort of results, based on the “stochastic calculus of variation” of Paul Malliavin.