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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Products of constant curvature spaces
with a Brownian independence property


Author: H. R. Hughes
Journal: Proc. Amer. Math. Soc. 126 (1998), 3417-3425
MSC (1991): Primary 58G32; Secondary 53B20, 60J65
MathSciNet review: 1459125
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Abstract | References | Similar Articles | Additional Information

Abstract: The time and place Brownian motion on the product of constant curvature spaces first exits a normal ball of radius $\epsilon $ centered at the starting point of the Brownian motion are considered. The asymptotic expansions, as $\epsilon $ decreases to zero, for joint moments of the first exit time and place random variables are computed with error $O(\epsilon ^{10})$. It is shown that the first exit time and place are independent random variables only if each factor space is locally flat or of dimension three.


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Additional Information

H. R. Hughes
Affiliation: Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901-4408
Email: hrhughes@math.siu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04447-5
PII: S 0002-9939(98)04447-5
Keywords: Brownian motion, symmetric space, exit time, exit place
Received by editor(s): February 3, 1997
Received by editor(s) in revised form: March 27, 1997
Communicated by: Stanley Sawyer
Article copyright: © Copyright 1998 American Mathematical Society