Fe b 20 08 Properties of the density for a three dimensional stochastic wave equation

We consider a stochastic wave equation in space dimension three driven by a noise white in time and with an absolutely continuous correlation measure given by the product of a smooth function and a Riesz kernel. Let p t,x (y) be the density of the law of the solution u(t, x) of such an equation at points (t, x) ∈]0, T ] × R 3. We prove that the mapping (t, x) → p t,x (y) owns the same regularity as the sample paths of the process {u(t, x), (t, x) ∈ ]0, T ]×R 3 } established in [5]. The proof relies on Malliavin calculus and more explicitely, the integration by parts formula of [17] and estimates derived form it.