| Título: | Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times |
| Autores: |
Bass, Richard F.; University of Washington Burdzy, Krzysztof; University of Washington |
| Fecha: | 1996-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics Brownian motion, eigenfunction expansion, eigenvalues, arcsine law. 60J65, 60J35, 60J45. |
| Descripción: | Let $B$ be a Borel subset of $R^d$ with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting $B$. Let $A_1$ be the time spent by Brownian motion in a closed cone with vertex $0$ until time one. We show that $\lim_{u\to 0} \log P^0(A_1 < u) /\log u = 1/\xi$ where $\xi$ is defined in terms of the first eigenvalue of the Laplacian in a compact domain. Eigenvalues of the Laplacian in open and closed sets are compared. |
| Idioma: | Inglés |
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