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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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.
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Table of contents (10 chapters)
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