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Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times


 
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1. Title Title of document Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times
 
2. Creator Author's name, affiliation, country Richard F. Bass; University of Washington
 
2. Creator Author's name, affiliation, country Krzysztof Burdzy; University of Washington
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Brownian motion, eigenfunction expansion, eigenvalues, arcsine law.
 
3. Subject Subject classification 60J65, 60J35, 60J45.
 
4. Description 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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7. Date (YYYY-MM-DD) 1996-01-31
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3
 
10. Identifier Digital Object Identifier 10.1214/EJP.v1-3
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 1
 
12. Language English=en en
 
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