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[null,"1.","Record Nr.",null,"UNISALENTO991002949169707536"]
[null,null,"Autore",null,"Burdzy, Krzysztof"]
[null,null,"Titolo",null,"Brownian motion and its applications to mathematical analysis [e-book] : École d'été de probabilités de Saint-Flour XLIII - 2013 / Krzysztof Burdzy"]
[null,null,"Pubbl/distr/stampa",null,"Cham [Switzerland] : Springer, 2014"]
[null,null,"ISBN",null,"9783319043944"]
[null,null,"Descrizione fisica",null,"1 online resource (xii, 137 pages)"]
[null,null,"Collana",null,"Lecture notes in mathematics, 1617-9692; 2106"]
[null,null,"Classificazione",null,"AMS 60-02"]
[{"$nulls":4},"AMS 60G17"]
[{"$nulls":4},"AMS 60H30"]
[{"$nulls":4},"AMS 60J65"]
[{"$nulls":4},"LC QA274.75"]
[null,null,"Disciplina",null,"530.475"]
[null,null,"Soggetti",null,"Brownian motion processes"]
[{"$nulls":4},"Mathematical analysis"]
[{"$nulls":4},"Stochastic analysis"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"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"]
[null,null,null,"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"]