Brownian Motion and its Applications to Mathematical Analysis

Ecole d'Ete de Probabilites de Saint-Flour XLIII - 2013

Serie: Ecole d'Ete de Probabilites de Saint-Flour 2106

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. Les mer
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Vår pris: 675,-

(Paperback) Fri frakt!
Leveringstid: Sendes innen 21 dager

Om boka

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.

Fakta

Innholdsfortegnelse

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.