2015 Volume 67 Issue 4 Pages 1605-1630
In this paper we consider a general class of second order stochastic partial differential equations on ℝd driven by a Gaussian noise which is white in time and has a homogeneous spatial covariance. Using the techniques of Malliavin calculus we derive the smoothness of the density of the solution at a fixed number of points (t,x1), …, (t,xn), t > 0, with some suitable regularity and nondegeneracy assumptions. We also prove that the density is strictly positive in the interior of the support of the law.
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