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.
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.
Brownian Motion and its Applications to Mathematical Analysis: École d'Été de Probabilités de Saint-Flour XLIII - 2013
Brownian Motion and its Applications to Mathematical Analysis: École d'Été de Probabilités de Saint-Flour XLIII - 2013
Product Details
| ISBN-13: | 9783319043944 |
|---|---|
| Publisher: | Springer-Verlag New York, LLC |
| Publication date: | 02/07/2014 |
| Series: | Lecture Notes in Mathematics , #2106 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| File size: | 4 MB |