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- Author: Krzysztof Burdzy
- Publisher: Springer-Verlag GmbH
- Year: 2014
- ISBN: 9783319043944
- ISBN-10: 3319043943
- ISBN-13: 9783319043944
- Format: PDF
- Language: English
Brownian Motion and its Applications to Mathematical Analysis (e-book) (used book) | bookbook.eu
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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.
- Author: Krzysztof Burdzy
- Publisher: Springer-Verlag GmbH
- Year: 2014
- ISBN: 9783319043944
- ISBN-10: 3319043943
- ISBN-13: 9783319043944
- Format: PDF
- Language: English 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.
Reviews