Skip to main content
SpringerLink
Log in
Book cover

Random Obstacle Problems

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

  • Book
  • © 2017

Overview

Authors:
  1. Lorenzo Zambotti

    1. Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, Paris, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Provides a self-contained presentation in a clear and pedagogical style
  • Includes a special chapter on Bessel processes with detailed discussions of results scattered across the literature
  • Offers an original point of view on a booming subject (SPDEs)

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

Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Lorenzo Zambotti
    Pages 1-11

  3. The Reflecting Brownian Motion

    • Lorenzo Zambotti
    Pages 13-30

  4. Bessel Processes

    • Lorenzo Zambotti
    Pages 31-57

  5. The Stochastic Heat Equation

    • Lorenzo Zambotti
    Pages 59-86

  6. Obstacle Problems

    • Lorenzo Zambotti
    Pages 87-108

  7. Integration by Parts Formulae

    • Lorenzo Zambotti
    Pages 109-140

  8. The Contact Set

    • Lorenzo Zambotti
    Pages 141-157

  9. Back Matter

    Pages 159-164
    Download chapter PDF
Back to top

Keywords

About this book

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.


Reviews

“This book is an excellent, rigorous monograph on stochastic partial differential equations with reflections at a boundary. … Engineers who struggle with numerical solutions of heat equations and Fokker-Plank equations in phase lock theory in white and colored noise will find this book useful. The author is a leading contributor to this field and has noted several open problems” (Nirode C. Mohanty, zbMATH 1386.60002, 2018)

“I found the book very well written and informative, with something interesting to be found on every page. ... The exercises throughout the text and the list of open problems at the end of each chapter make the book suitable for a special topics graduate course.” (Sergey V. Lototsky, Mathematical Reviews, December, 2017)

Authors and Affiliations

  • Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, Paris, France

    Lorenzo Zambotti

Bibliographic Information

  • Book Title: Random Obstacle Problems

  • Book Subtitle: École d'Été de Probabilités de Saint-Flour XLV - 2015

  • Authors: Lorenzo Zambotti

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-52096-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Softcover ISBN: 978-3-319-52095-7Published: 28 February 2017

  • eBook ISBN: 978-3-319-52096-4Published: 27 February 2017

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 162

  • Number of Illustrations: 18 b/w illustrations, 2 illustrations in colour

  • Topics: Probability Theory and Stochastic Processes

Publish with us

Policies and ethics

Back to top

Search

Navigation