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Brownian motion and its applications to mathematical analysis : École d'Été de Probabilités de Saint-Flour XLIII - 2013 / Krzysztof Burdzy
Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: Lecture notes in mathematics ; 2106Publisher: Cham ; Heidelberg [u.a.] : Springer, 2014Description: XII, 137 S. : Ill., graph. DarstISBN:- 9783319043937
- QA274.75
Contents:
Summary: 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 domainsSummary: 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 domainsPPN: PPN: 779895126
| Item type | Home library | Shelving location | Call number | Status | Barcode | |
|---|---|---|---|---|---|---|
| Freihandbestand ausleihbar | Fachbibliothek Mathematik | Bibliothek / frei aufgestellt | Lect. notes / 2106 | Available | 36343706090 |
Total holds: 0