Random Obstacle Problems
École d'Été de Probabilités de Saint-Flour XLV - 2015
Authors: ZAMBOTTI, LORENZO
Free Preview- 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)
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- About this book
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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
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“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)
- Table of contents (7 chapters)
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Introduction
Pages 1-11
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The Reflecting Brownian Motion
Pages 13-30
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Bessel Processes
Pages 31-57
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The Stochastic Heat Equation
Pages 59-86
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Obstacle Problems
Pages 87-108
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Table of contents (7 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Random Obstacle Problems
- Book Subtitle
- École d'Été de Probabilités de Saint-Flour XLV - 2015
- Authors
-
- LORENZO ZAMBOTTI
- Series Title
- École d'Été de Probabilités de Saint-Flour
- Series Volume
- 2181
- Copyright
- 2017
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG
- eBook ISBN
- 978-3-319-52096-4
- DOI
- 10.1007/978-3-319-52096-4
- Softcover ISBN
- 978-3-319-52095-7
- Series ISSN
- 0721-5363
- Edition Number
- 1
- Number of Pages
- IX, 162
- Number of Illustrations
- 18 b/w illustrations, 2 illustrations in colour
- Topics
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