Brownian Motion and its Applications to Mathematical Analysis: École d`Été de Probabilités de Saint-Flour XLIII – 2013
Krzysztof Burdzy, "Brownian Motion and its Applications to Mathematical Analysis: École d`Été de Probabilités de Saint-Flour XLIII – 2013"
English | ISBN: 3319043935 | 2014 | 152 pages | EPUB, PDF | 2 MB + 2 MB
English | ISBN: 3319043935 | 2014 | 152 pages | EPUB, PDF | 2 MB + 2 MB
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.