1.

Record Nr.

UNISALENTO991002949169707536

Autore

Burdzy, Krzysztof

Titolo

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

Pubbl/distr/stampa

Cham [Switzerland] : Springer, 2014

ISBN

9783319043944

Descrizione fisica

1 online resource (xii, 137 pages)

Collana

Lecture notes in mathematics, 1617-9692; 2106

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>

Disciplina

530.475

Soggetti

Brownian motion processes

Mathematical analysis

Stochastic analysis

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

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