(DOWNLOAD) "Brownian Motion and its Applications to Mathematical Analysis" by Krzysztof Burdzy ~ eBook PDF Kindle ePub Free
eBook details
- Title: Brownian Motion and its Applications to Mathematical Analysis
- Author : Krzysztof Burdzy
- Release Date : January 07, 2014
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 3978 KB
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.