SPD

Abstract

We consider a non-linear stochastic wave equation driven by a Gaussian noise white in time and with a spatial stationary covariance. From results of Dalang and Sanz-Solé (2009), it is known that the sample paths of the random field solution are Hölder continuous, jointly in time and in space. In this lecture, we will establish a characterization of the topological support of the law of the solution to this equation in Hölder norm. This will follow from an approximation theorem, in the convergence of probability, for a sequence of evolution equations driven by a family of regularizations of the driving noise.