Foundations of the theory of semilinear stochastic partial differential equations

Abstract

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.

36 pages

References in corpus (3)

• An alternative approach on the existence of affine realizations for HJM term structure models
• Some refinements of existence results for SPDEs driven by Wiener processes and Poisson random measures
• Existence of affine realizations for Lévy term structure models