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＜E-Book＞
A Concise Course on Stochastic Partial Differential Equations / by Claudia Prévôt, Michael Röckner
(Lecture Notes in Mathematics. ISSN:16179692 ; 1905)

Edition	1st ed. 2007.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2007
Language	English
Size	VI, 148 p : online resource
Authors	*Prévôt, Claudia author Röckner, Michael author SpringerLink (Online service)
Subjects	LCSH:Mathematical analysis LCSH:Differential equations LCSH:Probabilities FREE:Analysis FREE:Differential Equations FREE:Probability Theory
Notes	Motivation, Aims and Examples -- Stochastic Integral in Hilbert spaces -- Stochastic Differential Equations in Finite Dimensions -- A Class of Stochastic Differential Equations in Banach Spaces -- Appendices: The Bochner Integral -- Nuclear and Hilbert-Schmidt Operators -- Pseudo Invers of Linear Operators -- Some Tools from Real Martingale Theory -- Weak and Strong Solutions: the Yamada-Watanabe Theorem -- Strong, Mild and Weak Solutions These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices HTTP:URL=https://doi.org/10.1007/978-3-540-70781-3

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