Overview
- 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)
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Table of contents (7 chapters)
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
“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
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
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