Lecture Notes in Mathematics

A Concise Course on Stochastic Partial Differential Equations

Authors: Prévôt, Claudia, Röckner, Michael

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  • A concise and as self-contained as possible an introduction to the "variational approach"
  • A large part of necessary background material is included in appendices
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  • ISBN 978-3-540-70781-3
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About this book

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.

Reviews

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 Högele, Zentralblatt MATH, Vol. 1123 (1), 2008)


Table of contents (4 chapters)

Table of contents (4 chapters)
  • Motivation, Aims and Examples

    Pages 1-4

  • Stochastic Integral in Hilbert Spaces

    Pages 5-42

  • Stochastic Differential Equations in Finite Dimensions

    Pages 43-54

  • A Class of Stochastic Differential Equations

    Pages 55-103

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-540-70781-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-3-540-70780-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Concise Course on Stochastic Partial Differential Equations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1905
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-70781-3
DOI
10.1007/978-3-540-70781-3
Softcover ISBN
978-3-540-70780-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VI, 148
Topics