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Brownian Motion and its Applications to Mathematical Analysis : Ecole d'Ete de Probabilites de Saint-Flour XLIII - 2013. 2014 ed..
・ISBN 978-3-319-04393-7 paper EUR 49.99
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| 著者・編者 | Burdzy, Krzysztof, |
|---|---|
| シリーズ | Lecture Notes in Mathematics |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2014 |
| ページ数 | 137 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-24457＞ |
解説
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.