A Concise Course on Stochastic Partial Differential Equations

Claudia Prévot

ISBN 10: 3540707808 / ISBN 13: 9783540707806

Verlag: Springer, Berlin, Springer Berlin Heidelberg, Springer, 2007

Beschreibung

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 148 pp. Englisch.

Bestandsnummer des Verkäufers 9783540707806

Bibliografische Details

• Titel: A Concise Course on Stochastic Partial Differential Equations
• Verlag: Springer, Berlin, Springer Berlin Heidelberg, Springer
• Erscheinungsjahr: 2007
• Sprache: Englisch
• ISBN-10: 3540707808
• ISBN-13: 9783540707806
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 234B x 156 H x 9 T Millimeter Breite: 234 mm, Höhe: 156 mm, Tiefe: 9 mm
• Gewicht: 260 Gramm

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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.