Stochastic volterra equations in the plane: smoothness of the law

Abstract

We give sufficient conditions ensuring the smoothness of the density for the law of the solution of Volterra equations in the plane. One of the motivations for the study of such class of equations is provided by non-linear hyperbolic stochastic partial differential equations appearing in the construction of some path-valued processes on manifolds. The proof is based on Malliavin Calculus.