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Brownian Motion and its Applications to Mathematical Analysis : École d'Été de Probabilités de Saint-Flour XLIII – 2013 / by Krzysztof Burdzy.
Springer Nature - Springer Mathematics and Statistics (R0) eBooks 2014 English International Available online
View online- Format:
- Book
- Conference/Event
- Author/Creator:
- Burdzy, K. (Krzysztof), Author.
- Conference Name:
- Ecole d'été de probabilités de Saint-Flour (43rd : 2013 : Saint Flour, France)
- Series:
- École d'Été de Probabilités de Saint-Flour, 0721-5363 ; 2106
- Language:
- English
- Subjects (All):
- Probabilities.
- Differential equations, Partial.
- Potential theory (Mathematics).
- Probability Theory and Stochastic Processes.
- Partial Differential Equations.
- Potential Theory.
- Local Subjects:
- Probability Theory and Stochastic Processes.
- Partial Differential Equations.
- Potential Theory.
- Physical Description:
- 1 online resource (XII, 137 p. 16 illus., 4 illus. in color.)
- Edition:
- 1st ed. 2014.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2014.
- Language Note:
- English
- Summary:
- 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.
- 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.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references (pages 133-137).
- ISBN:
- 3-319-04394-3
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