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arXiv:1907.02352 [math.PR]AbstractReferencesReviewsResources

Foundations of the theory of semilinear stochastic partial differential equations

Stefan Tappe

Published 2019-07-04Version 1

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.

Comments: 36 pages
Journal: International Journal of Stochastic Analysis, vol. 2013, Article ID 798549, 25 pages
Categories: math.PR, math.FA
Subjects: 60H15, 60G17
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