Introduction and Motivating Examples

Abstract

Stochastic differential equations are well known to model stochastic processes observed in the study of dynamic systems arising from many areas of science, engineering, and finance. Existence and uniqueness of mild, strong, relaxed, and weak solutions; stability, stabilizability, and control problems; regularity and continuous dependence on initial values; approximation problems notably of Yosida; among others, of solutions of stochastic differential equations in infinite dimensions have been investigated by several authors, see, for instance, Ahmed [1, 6, 8] Bharucha-Reid [1], Curtain and Pritchard [1], Da Prato [2], Da Prato and Zabczyk [1, 3, 4], Gawarecki and Mandrekar [1], Kotelenez [1], Liu [2], Mandrekar and Rüdiger [1], McKibben [2], and Prévôt and Röckner [1] and the references therein. Yosida approximations play a key role in many of these problems.