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Random Obstacle Problems

École d'Été de Probabilités de Saint-Flour XLV - 2015

  • Lorenzo Zambotti

Part of the Lecture Notes in Mathematics book series (LNM, volume 2181)

Also part of the École d'Été de Probabilités de Saint-Flour book sub series (LNMECOLE, volume 2181)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Lorenzo Zambotti
    Pages 1-11
  3. Lorenzo Zambotti
    Pages 13-30
  4. Lorenzo Zambotti
    Pages 31-57
  5. Lorenzo Zambotti
    Pages 59-86
  6. Lorenzo Zambotti
    Pages 87-108
  7. Lorenzo Zambotti
    Pages 109-140
  8. Lorenzo Zambotti
    Pages 141-157
  9. Back Matter
    Pages 159-164

About this book

Introduction

Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with reflection at a boundary, this book begins with a discussion of classical one-dimensional diffusions as the reflecting Brownian motion, devoting a chapter to Bessel processes, and moves on to function-valued solutions to SPDEs. Inspired by the classical stochastic calculus for diffusions, which is unfortunately still unavailable in infinite dimensions, it uses integration by parts formulae on convex sets of paths in order to describe the behaviour of the solutions at the boundary and the contact set between the solution and the obstacle. The text may serve as an introduction to space-time white noise, SPDEs and monotone gradient systems. Numerous open research problems in both classical and new topics are proposed.


Keywords

Reflection on an obstacle Stochastic partial differential equations Brownian motion Local time Integrations by parts formulae

Authors and affiliations

  • Lorenzo Zambotti
    • 1
  1. 1.Laboratoire de Probabilités et Modèles AléatoiresUniversité Pierre et Marie CurieParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-52096-4
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-52095-7
  • Online ISBN 978-3-319-52096-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site