E-Book, Englisch, Band 1905, 148 Seiten, eBook
Reihe: Lecture Notes in Mathematics
Prévôt / Röckner A Concise Course on Stochastic Partial Differential Equations
Erscheinungsjahr 2007
ISBN: 978-3-540-70781-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 1905, 148 Seiten, eBook
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-70781-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
