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International Journal of Stochastic Analysis
Volume 2013, Article ID 798549, 25 pages
http://dx.doi.org/10.1155/2013/798549
Review Article

Foundations of the Theory of Semilinear Stochastic Partial Differential Equations

Leibniz Universität Hannover, Institut für Mathematische Stochastik, Welfengarten 1, 30167 Hannover, Germany

Received 28 May 2013; Accepted 16 August 2013

Academic Editor: Hong-Kun Xu

Copyright © 2013 Stefan Tappe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.