Abstract stochastic evolution equations in M-type 2 Banach spaces

Abstract

This paper devotes to studying abstract stochastic evolution equations in M-type 2 Banach spaces. First, we handle nonlinear evolution equations with multiplicative noise. The existence and uniqueness of local and global mild solutions under linear growth and Lipschitz conditions on coefficients are presented. The regular dependence of solutions on initial data is also studied. Second, we investigate linear evolution equations with additive noise. The existence and uniqueness of strict and mild solutions and their regularity are shown. Finally, we explore semilinear evolution equations with additive noise. We concentrate on the existence, uniqueness and regular dependence of solutions on initial data.