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Record Nr. |
UNISA996466625903316 |
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Autore |
Prévôt Claudia |
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Titolo |
A concise course on stochastic partial differential equations / / Claudia Prévôt, Michael Röckner |
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Pubbl/distr/stampa |
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Berlin, Germany ; ; New York, New York : , : Springer, , [2007] |
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©2007 |
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ISBN |
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1-280-90216-7 |
9786610902163 |
3-540-70781-6 |
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Edizione |
[1st ed. 2007.] |
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Descrizione fisica |
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1 online resource (148 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1905 |
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Disciplina |
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Soggetti |
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Stochastic differential equations |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. 137-139) and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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