Introduction and Motivating Examples

Stochastic differential equations, in the sense of Itô, arise quite naturally as mathematical models in many areas of science, engineering and finance. Problems such as existence and uniqueness of mild solutions; stability and optimal control; continuous dependence on initial values; Yosida and Trotter-Kato approximations, among others, of mild solutions of stochastic differential equations in infinite-dimensional spaces have been investigated by many authors, see Ahmed [1, 2], Bharucha-Reid [1], Curtain and Pritchard [1], Da Prato [1], Da Prato and Zabczyk [1, 3, 4], Gawarecki and Mandrekar [1], Govindan [13], Itô [2], Kallianpur and Xiong [1], Kotelenez [1], Liu [1], Liu and Röckner [1], Lototsky and Rozovsky [1], Mandrekar and Rüdiger [1], McKibben [2], Métivier [2], Peszat and Zabczyk [1] and Prévôt and Röckner [1], to mention only a few, and the references cited therein.