A Concise Course on Stochastic Partial Differential Equations

di Claudia Prévôt (Autore)

Michael Röckner (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2007

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.

• Autore: Claudia Prévôt, Michael Röckner
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Lecture Notes in Mathematics
• Anno: 2007
• Rilegatura: Paperback / softback
• Pagine: 148 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783540707806

Testo in English