A Concise Course on Stochastic Partial Differential Equations (Lecture Notes in Mathematics, 1905)

Prévôt, Claudia

ISBN 10: 3540707808 / ISBN 13: 9783540707806

Verlag: Springer, 2007

Beschreibung

Bestandsnummer des Verkäufers ABLIING23Mar3113020175305

Bibliografische Details

• Titel: A Concise Course on Stochastic Partial Differential Equations (Lecture Notes in Mathematics, 1905)
• Verlag: Springer
• Veröffentlichungsdatum: 2007
• Sprache: Englisch
• ISBN-10: 3540707808
• ISBN-13: 9783540707806
• Bindung: Softcover
• Zustand: New

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Inhaltsangabe

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are 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 is included in appendices.

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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 results from the theory of Hilbert spaces, are included in appendices.