Analysis of the density of the solution to a semilinear SPDE with fractional noise

Abstract

In this paper, we consider a general class of semilinear stochastic partial differential equations driven by a two-parameter fractional-coloured noise with Hurst index bigger than one half. Using the techniques of Malliavin calculus, we analyze the properties of the density of the solution. In particular, we establish lower and upper Gaussian-type bounds for the probability density of the mild solution at any fixed point and we prove the smoothness of this density.