A malliavin calculus method to study densities of additive functionals of SDE's with irregular drifts

Abstract

We present a general method which allows to use Malliavin Calculus for additive functionals of stochastic equations with irregular drift. This method uses the Girsanov theorem combined with Itô-Taylor expansion in order to obtain regularity properties for this density. We apply the methodology to the case of the Lebesgue integral of a diffusion with bounded and measurable drift. © Association des Publications de l'Institut Henri Poincaré, 2012.