Stochastic Differential Equations in Hilbert Space and their Application to Delay Systems

Abstract

We consider infinite dimensional stochastic differential equations with state dependent martingale noise using semigroup approach. Several kinds of solutions to such equations are studied and the interrelationsbetween them investigated. We prove also some existence theorems for a general class of stochastic evolution equations. New results on equations with state dependent Gaussian white noise are obtained. The general theory is applied to stochastic delay equations with state dependent noise. A representation theorem as well as an existence and uniqueness theorem for such equations are proved.