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1996 Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times
Richard Bass, Krzysztof Burdzy
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Electron. J. Probab. 1: 1-19 (1996). DOI: 10.1214/EJP.v1-3

Abstract

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.

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Richard Bass. Krzysztof Burdzy. "Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times." Electron. J. Probab. 1 1 - 19, 1996. https://doi.org/10.1214/EJP.v1-3

Information

Accepted: 31 January 1996; Published: 1996
First available in Project Euclid: 25 January 2016

zbMATH: 0891.60079
MathSciNet: MR1386295
Digital Object Identifier: 10.1214/EJP.v1-3

Subjects:
Primary: 60J65
Secondary: 60J35 , 60J45

Keywords: arcsine law , Brownian motion , eigenfunction expansion , Eigenvalues

Vol.1 • 1996
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