Brownian Motion and its Applications to Mathematical Analysis École d'Été de Probabilités de Saint-Flour XLIII - 2013 /

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, su...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Burdzy, Krzysztof (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2014.
Edición:1st ed. 2014.
Colección:École d'Été de Probabilités de Saint-Flour ; 2106
Temas:
Probabilities.
Differential equations.
Potential theory (Mathematics).
Probability Theory.
Differential Equations.
Potential Theory.
Acceso en línea:Texto Completo

MARC

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300 |a XII, 137 p. 16 illus., 4 illus. in color.  |b online resource. 
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490 1 |a École d'Été de Probabilités de Saint-Flour ;  |v 2106 
505 0 |a 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. 
520 |a 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. 
650 0 |a Probabilities. 
650 0 |a Differential equations. 
650 0 |a Potential theory (Mathematics). 
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650 2 4 |a Differential Equations. 
650 2 4 |a Potential Theory. 
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950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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