ENGLISH

A concise course on stochastic partial differential equations

By Claudia Prévôt , Michael Röckner (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2007
ISBN
9783540707806, 3540707808
DOI
10.1007/978-3-540-70781-3
ISSN
0075-8434
Open Library ID
OL20268237M
Language
english
Format
PDF
Filesize
2 MB (1652369 bytes)
Series
Lecture notes in mathematics 1905
Edition
1
Pages
148\148
Time added
2010-02-18 13:16:04
Partial Differential Equations; Probability Theory

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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