Brownian Motion and its Applications to Mathematical Analysis [[electronic resource] ] : École d'Été de Probabilités de Saint-Flour XLIII – 2013 / / by Krzysztof Burdzy
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| Autore: |
Burdzy Krzysztof
|
| Titolo: |
Brownian Motion and its Applications to Mathematical Analysis [[electronic resource] ] : École d'Été de Probabilités de Saint-Flour XLIII – 2013 / / by Krzysztof Burdzy
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
| Edizione: | 1st ed. 2014. |
| Descrizione fisica: | 1 online resource (XII, 137 p. 16 illus., 4 illus. in color.) |
| Disciplina: | 530.475 |
| Soggetto topico: | Probabilities |
| Partial differential equations | |
| Potential theory (Mathematics) | |
| Probability Theory and Stochastic Processes | |
| Partial Differential Equations | |
| Potential Theory | |
| Classificazione: | MAT 606f |
| MAT 607f | |
| SI 850 | |
| 60J6560H3060G17 | |
| Note generali: | Bibliographic Level Mode of Issuance: Monograph |
| Nota di bibliografia: | Includes bibliographical references (pages 133-137). |
| Nota di contenuto: | 1. Brownian motion -- 2. Probabilistic proofs of classical theorems -- 3. Overview of the "hot spots" problem -- 4. Neumann eigenfunctions and eigenvalues -- 5. Synchronous and mirror couplings -- 6. Parabolic boundary Harnack principle -- 7. Scaling coupling -- 8. Nodal lines -- 9. Neumann heat kernel monotonicity -- 10. Reflected Brownian motion in time dependent domains. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Brownian motion and its applications to mathematical analysis |
| ISBN: | 3-319-04394-3 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 996205178603316 |
| Lo trovi qui: | Univ. di Salerno |
| Opac: | Controlla la disponibilità qui |
Serie:
École d'Été de Probabilités de Saint-Flour, . 0721-5363 ; ; 2106