Marta Sanz-Sole (University of Barcelona )

Approximations and support of Wiener functionals: applications to stochastic waves

Abstract: The connection between the characterization of the topological support of the law of a random vector and approximation schemes is already visible in the classical result for diffusion processes by Stroock and Varadhan (1972). In the framework of an abstract Wiener space, this is set up more explicitly by Aida, Kusuoka and Stroock (1993). In this talk, we will consider a class of stochastic wave equations driven by a Gaussian spatially stationary noise. We will present an approximation result by a sequence of stochastic partial differential equations obtained by smoothing the noise. As a consequence, a characterization of the support of the law of the solution in Hölder norm will be derived. We shall also briefly report on other applications, like the asymptotics of the density of small perturbations of the initial equation.