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A Concise Course on Stochastic Partial Differential Equations / by Claudia Prévôt, Michael Röckner
(Lecture Notes in Mathematics. ISSN:16179692 ; 1905)
版 | 1st ed. 2007. |
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出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2007 |
本文言語 | 英語 |
大きさ | VI, 148 p : online resource |
著者標目 | *Prévôt, Claudia author Röckner, Michael author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Differential equations LCSH:Probabilities FREE:Analysis FREE:Differential Equations FREE:Probability Theory |
一般注記 | 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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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783540707813 |
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EB00235987 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000117988 |
ISBN | 9783540707813 |
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