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École d'Été de Probabilités de Saint-Flour

Random Obstacle Problems

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

Authors: ZAMBOTTI, LORENZO

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  • 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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eBook $39.99
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  • ISBN 978-3-319-52096-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
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  • Immediate eBook download after purchase
Softcover $49.99
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  • ISBN 978-3-319-52095-7
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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)

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $39.99
price for Mexico (gross)
  • ISBN 978-3-319-52096-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for Mexico
  • ISBN 978-3-319-52095-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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
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