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

DOI:
https://doi.org/10.1090/S0002-9939-98-04447-5

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 centered at the starting point of the Brownian motion are considered. The asymptotic expansions, as decreases to zero, for joint moments of the first exit time and place random variables are computed with error . 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:
https://doi.org/10.1090/S0002-9939-98-04447-5

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