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Cover: 9783540707806 | A Concise Course on Stochastic Partial Differential Equations | Buch
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A Concise Course on Stochastic Partial Differential Equations
Taschenbuch von Claudia Prévot (u. a.)
Sprache: Englisch

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Beschreibung
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 [...] 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.

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 [...] 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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2007
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: vi
148 S.
ISBN-13: 9783540707806
ISBN-10: 3540707808
Sprache: Englisch
Herstellernummer: 978-3-540-70780-6
Einband: Kartoniert / Broschiert
Autor: Prévot, Claudia
Röckner, Michael
Hersteller: Springer
Springer, Berlin
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Abbildungen: VI, 148 p.
Maße: 8 x 155 x 235 mm
Von/Mit: Claudia Prévot (u. a.)
Erscheinungsdatum: 08.06.2007
Gewicht: 0,26 kg
Artikel-ID: 102056994
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