Stochastic Partial Differential Equations Driven by Spatially Homogeneous Gaussian Noise

The purpose of the rest of this book is to apply the criteria established in Chapter 5 to random vectors which are solutions of SPDE’s. As preliminaries, we give in this chapter a result on existence and uniqueness of solutions for a general type of equations that cover all the cases we shall encounter. We start by introducing the stochastic integral to be used in the rigourous formulation of the SPDE’s and in the application of the Malliavin differential calculus. This is an extension of the integral studied in reference [14] and developed in reference [54].