Brownian motion and its applications to mathematical analysis: école d'été de probabilités de Saint-Flour XLIII-2013 / Krzysztof Burdzy

Collectivité principale: école d'été de probabilités de Saint-Flour, 43, Saint-Flour (2013) Co-auteur: Burdzy, Krzysztof (1957-) - AuteurType de document: CongrèsCollection: Lecture notes in mathematics, école d'été de probabilités de Saint-Flour ; 2106Langue: anglaisPays: SwisseÉditeur: Cham : Springer, cop. 2014Description: 1 vol. (XII-137 p.) : fig. ; 24 cm ISBN: 9783319043937 ; br. Résumé: 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. (Source : Springer).Bibliographie: Bibliogr. p. 133-137. Sujets MSC: 60J65 Probability theory and stochastic processes -- Markov processes -- Brownian motion
60H30 Probability theory and stochastic processes -- Stochastic analysis -- Applications of stochastic analysis (to PDE, etc.)
60G17 Probability theory and stochastic processes -- Stochastic processes -- Sample path properties
58J65 Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Diffusion processes and stochastic analysis on manifolds
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Bibliogr. p. 133-137

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. (Source : Springer)

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