A Concise Course on Stochastic Partial Differential Equations

A Concise Course on Stochastic Partial Differential Equations
(Lecture Notes in Mathematics)
By Claudia Prévôt,&nbspMichael Röckner,

• Publisher: Springer
• Number Of Pages: 148
• Publication Date: 2007-07
• Sales Rank: 3606861
• ISBN / ASIN: 3540707808
• EAN: 9783540707806
• Binding: Paperback
• Manufacturer: Springer
• Studio: Springer
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Book Description:

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.

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