Abstract stochastic evolution equations in M-type 2 Banach spaces

TL;DR

This paper investigates stochastic evolution equations in M-type 2 Banach spaces, establishing existence, uniqueness, and regularity of solutions for various types of equations with multiplicative and additive noise.

Contribution

It provides new results on the existence, uniqueness, and regular dependence of solutions for nonlinear, linear, and semilinear stochastic evolution equations in M-type 2 Banach spaces.

Findings

Existence and uniqueness of local and global mild solutions.

Regular dependence of solutions on initial data.

Solutions' regularity for linear and semilinear equations.

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.