Brownian Motion and its Applications to Mathematical Analysis École d'Été de Probabilités de Saint-Flour XLIII – 2013 /
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, su...
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| Formato: | Recurso Eletrônico livro eletrônico |
| Idioma: | English |
| Publicado em: |
Cham :
Springer International Publishing : Imprint: Springer,
2014.
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| Edição: | 1st ed. 2014. |
| coleção: | École d'Été de Probabilités de Saint-Flour,
2106 |
| Assuntos: | |
| Acesso em linha: | https://doi.org/10.1007/978-3-319-04394-4 |
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Sumário:
- 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.