Note on abstract stochastic semilinear evolution equations

TL;DR

This paper investigates the existence, regularity, and dependence of solutions for abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces, and discusses applications to stochastic PDEs.

Contribution

It establishes the existence and regularity of solutions, and their dependence on initial data, for a class of stochastic semilinear evolution equations, with applications to stochastic PDEs.

Findings

Existence of unique local mild solutions

Regularity of solutions

Continuous dependence on initial data

Abstract

This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular dependence of the solutions on initial data. Finally, some applications to stochastic partial differential equations are presented.