Brownian Motion and its Applications to Mathematical Analysis
École d'Été de Probabilités de Saint-Flour XLIII – 2013
Nonfiction, Science & Nature, Mathematics, Differential Equations, Statistics
| Author: | Krzysztof Burdzy | ISBN: | 9783319043944 |
| Publisher: | Springer International Publishing | Publication: | February 7, 2014 |
| Imprint: | Springer | Language: | English |
| Author: | Krzysztof Burdzy |
| ISBN: | 9783319043944 |
| Publisher: | Springer International Publishing |
| Publication: | February 7, 2014 |
| Imprint: | Springer |
| Language: | English |
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.
