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Record Nr. |
UNISALENTO991002949319707536 |
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Autore |
Burdzy, Krzysztof |
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Titolo |
Brownian motion and its applications to mathematical analysis : École d'été de probabilités de Saint-Flour XLIII - 2013 / Krzysztof Burdzy |
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Pubbl/distr/stampa |
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Cham [Switzerland] : Springer, c2014 |
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ISBN |
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Descrizione fisica |
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xii, 137 p. : ill. (some color) ; 24 cm |
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Collana |
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Lecture notes in mathematics, 0075-8434 ; 2106 |
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Classificazione |
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AMS 60-02 |
AMS 60G17 |
AMS 60H30 |
AMS 60J65 |
LC QA274.75 |
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Altri autori (Convegni) |
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École d'été de probabilités de Saint-Flour <43. ; 2013 ; Saint Flour, France> |
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Disciplina |
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Soggetti |
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Brownian motion processes |
Mathematical analysis |
Stochastic analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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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 |
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