An edition of Brownian Motion And Its Applications To Mathematical Analysis Cole Dt De Probabilits De Saintflour Xliii 2013 (2014)
Brownian Motion And Its Applications To Mathematical Analysis Cole Dt De Probabilits De Saintflour Xliii 2013
By Krzysztof Burdzy
Publish Date
2014
Publisher
Springer
Language
eng
Pages
137
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.