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Brownian motion and its applications to mathematical analysis École d'Été de Probabilités de Saint-Flour XLIII - 2013 / Krzysztof Burdzy.
| Author/creator | Burdzy, K. |
| Other author | Ecole d'été de probabilités de Saint-Flour 2013 : Saint Flour, France) |
| Format | Electronic |
| Publication Info | Cham ; New York : Springer, [2014] |
| Description | xii, 137 pages : illustrations ; 24 cm. |
| Supplemental Content | Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2014 English International |
| Supplemental Content | Full text available from Springer Books |
| Supplemental Content | Full text available from SpringerLINK Lecture Notes in Mathematics Contemporary (1997-present) |
| Subjects |
| Series | Lecture notes in mathematics, 0075-8434 ; 2106 Lecture notes in mathematics (Springer-Verlag) ; 2106. 0075-8434 |
| Contents | Brownian motion -- Probabilistic proofs of classical theorems -- Overview of the "hot spots" problem -- Neumann eigenfunctions and eigenvalues -- Synchronous and mirror couplings -- Parabolic boundary Harnack principle -- Scaling coupling -- Nodal lines -- Neumann heat kernel monotonicity -- Reflected Brownian motion in time dependent domains. |
| Abstract | 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.-- Source other than the Library of Congress. |
| Bibliography note | Includes bibliographical references (pages 133-137). |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2014931653 |
| ISBN | 9783319043937 (pbk.) |
| ISBN | 3319043935 (pbk.) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | ✔ Available |