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A Concise Course on Stochastic Partial Differential Equations

  • Claudia Prévôt
  • Michael Röckner

Part of the Lecture Notes in Mathematics book series (LNM, volume 1905)

Table of contents

About this book

Introduction

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.

Keywords

Bochner integral Yamada-Watanabe theorem invariant measures partial differential equation stochastic integrals in Hilbert space stochastic partial differential equations variational approach

Authors and affiliations

  • Claudia Prévôt
    • 1
  • Michael Röckner
    • 2
    • 3
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  3. 3.Departments of Mathematics and StatisticsPurdue UniversityWest LafayetteUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-70781-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-70780-6
  • Online ISBN 978-3-540-70781-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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