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Record Nr. |
UNINA9910300143903321 |
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Autore |
Burdzy Krzysztof |
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Titolo |
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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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
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ISBN |
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Edizione |
[1st ed. 2014.] |
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Descrizione fisica |
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1 online resource (XII, 137 p. 16 illus., 4 illus. in color.) |
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Collana |
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École d'Été de Probabilités de Saint-Flour, , 0721-5363 ; ; 2106 |
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Classificazione |
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MAT 606f |
MAT 607f |
SI 850 |
60J6560H3060G17 |
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Disciplina |
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Soggetti |
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Probabilities |
Partial differential equations |
Potential theory (Mathematics) |
Probability Theory and Stochastic Processes |
Partial Differential Equations |
Potential Theory |
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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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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (pages 133-137). |
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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 |
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