Lecture Notes in Mathematics: École d'Été de Probabilités de Saint-Flour XLIII – 2013

Burdzy, Krzysztof

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.

Details

Published by: Springer

Publication Date: 2014-02-20

Format: Paperback

ISBN-13: 9783319043937

DOI: 10.1007/978-3-319-04394-4

Dimensions: 235cm x155cm

Pages: 137