Foundations of the Theory of Semilinear Stochastic Partial Differential Equations. (27th November 2013)

• Record Type: Journal Article
• Authors: Tappe, Stefan
• Other Names: Xu Hong-Kun Academic Editor.
• Is Part Of: International journal of stochastic analysis. Volume 2013(2013)
• Publication Date: 2013-11-27
• Subjects: Stochastic analysis -- Periodicals; Stochastic analysis; Periodicals; 519.22
• DOI: 10.1155/2013/798549
• Languages: English
• ISSNs: 2090-3332

Abstract

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.