ABSTRACT
We begin by recalling some basic definitions and preliminaries, especially those on stochastic integration and stochastic differential equations in infinite dimensional spaces. We recall important inequalities for stochastic integrals with respect to Wiener processes which are essential for the subsequent developments. We also establish two notions of solutions, strong and mild, and investigate the existence and uniqueness of these two kinds of solutions under suitable assumptions. To present the proofs of all of these results here would require preparatory background material which would considerably increase both the size and scope of this book. Therefore, we would like to adopt the approach of omitting the proofs of those results which are treated in detail in well-known standard books, such as Da Prato and Zabczyk [1], Rozovskii [1] and Me´tivier [1]. However, those proofs will be presented which are not available in existing books and are to be found scattered in the literature, or which discuss ideas specially relevant to our purposes.
