Approximation and Support Theorem for a Wave Equation in Two Space Dimensions

Abstract

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space.The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise.For some particular classes of coef®cients, approximation in the L p -norm for p > 1 is also proved.