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

• Autore: Burdzy, Krzysztof
• Pubblicazione: Cham [Switzerland] : Springer, c2014
• Descrizione fisica: xii, 137 p. : ill. (some color) ; 24 cm
• Disciplina: 530.475
• Soggetto topico: Brownian motion processes; Mathematical analysis; Stochastic analysis
• Classificazione: AMS 60-02; AMS 60G17; AMS 60H30; AMS 60J65; LC QA274.75
• Altri autori (Convegni): École d'été de probabilités de Saint-Flour <43. ; 2013 ; Saint Flour, France>
• Nota di contenuto: 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
• 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
• ISBN: 9783319043937
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 991002949319707536
• Lo trovi qui: Univ. del Salento
• Serie: Lecture notes in mathematics, 0075-8434 ; 2106