Brownian Motion and its Applications to Mathematical Analysis: École d'Été de Probabilités de Saint-Flour XLIII – 2013
Author:   Krzysztof Burdzy
Publisher:   Springer International Publishing AG
Edition:   2014 ed.
Volume:   2106
ISBN:  

9783319043937


Pages:   137
Publication Date:   20 February 2014
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Brownian Motion and its Applications to Mathematical Analysis: École d'Été de Probabilités de Saint-Flour XLIII – 2013


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Overview

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.

Full Product Details

Author:   Krzysztof Burdzy
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   2014 ed.
Volume:   2106
Dimensions:   Width: 15.50cm , Height: 0.80cm , Length: 23.50cm
Weight:   2.409kg
ISBN:  

9783319043937


ISBN 10:   3319043935
Pages:   137
Publication Date:   20 February 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

"1. Brownian motion.- 2. Probabilistic proofs of classical theorems.- 3. Overview of the ""hot spots"" problem.- 4. Neumann eigenfunctions and eigenvalues.- 5. Synchronous and mirror couplings.- 6. Parabolic boundary Harnack principle.- 7. Scaling coupling.- 8. Nodal lines.- 9. Neumann heat kernel monotonicity.- 10. Reflected Brownian motion in time dependent domains."

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