Concise Course on Stochastic Partial Differential Equations

Häftad, Engelska, 2007

Del i serien Lecture Notes in Mathematics

441 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2007-06-08
Mått:155 x 235 x undefined mm
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:148
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540707806

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

From the reviews: "This monograph is an elegantly and economically written first introduction to the field and meets the expectations of the title entirely. A great advantage of this account; is its wide self-containance of the plot, the completeness of all proofs, as well as a nice overview over the different notions of solutions of SPDEs culminating in the Yamada-Watanabe theorem entirely proven in the appendix. This book might be particularly helpful for graduate students and young researchers to get acquainted with this sophisticated area of research." (Micheal Hogele, Zentralblatt MATH, Vol. 1123 (1), 2008)

Innehållsförteckning

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.