Foundations of the Theory of Semilinear Stochastic Partial Differential Equations

Abstract EN

The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations.

In particular, we provide a detailed study of the concepts of strong, weak, and mild solutions, establish their connections, and review a standard existence and uniqueness result.

The proof of the existence result is based on a slightly extended version of the Banach fixed point theorem.