Overview
- Contains interesting examples of couplings
- Gentle introduction to Brownian motion and analysis
- Heuristic explanations of the main results
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2106)
Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
These lecture notes provide an introduction to the applications of Brownian motion to analysis and more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics.
The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domains.
Authors and Affiliations
Bibliographic Information
Book Title: Brownian Motion and its Applications to Mathematical Analysis
Book Subtitle: École d'Été de Probabilités de Saint-Flour XLIII – 2013
Authors: Krzysztof Burdzy
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-04394-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Softcover ISBN: 978-3-319-04393-7Published: 20 February 2014
eBook ISBN: 978-3-319-04394-4Published: 07 February 2014
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 137
Number of Illustrations: 12 b/w illustrations, 4 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Partial Differential Equations, Potential Theory
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