Random Obstacle Problems / Lecture Notes in Mathematics Bd.2181 (PDF)
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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.
- Autor: Lorenzo Zambotti
- 2017, 1st ed. 2017, 162 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319520962
- ISBN-13: 9783319520964
- Erscheinungsdatum: 27.02.2017
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- Größe: 2.61 MB
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“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)
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