ENGLISH

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

By Krzysztof Burdzy (auth.)

Book information

Publisher
Springer International Publishing
Year
2014
ISBN
978-3-319-04393-7, 978-3-319-04394-4
DOI
10.1007/978-3-319-04394-4
Language
english
Format
PDF
Filesize
2 MB (1627938 bytes)
Series
Lecture Notes in Mathematics 2106 École d'Été de Probabilités de Saint-Flour
Edition
1
Pages
137\145
Time added
2014-04-13 05:00:00
Probability Theory and Stochastic Processes; Parti

Description

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.

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