Format:
Online-Ressource (VI, 144 p, digital)
ISBN:
9783540707813
Series Statement:
SpringerLink
Content:
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.
Content:
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.
Note:
Includes bibliographical references (p. 137-139) and index
Additional Edition:
ISBN 9783540707806
Additional Edition:
Buchausg. u.d.T. Prévôt, Claudia A concise course on stochastic partial differential equations Berlin, Heidelberg [u.a.] : Springer, 2007 ISBN 3540707808
Additional Edition:
ISBN 9783540707806
Language:
English
Subjects:
Mathematics
Keywords:
Stochastische partielle Differentialgleichung
DOI:
10.1007/978-3-540-70781-3
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Röckner, Michael 1956-
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