## Products of constant curvature spaces with a Brownian independence property

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- by H. R. Hughes PDF
- Proc. Amer. Math. Soc.
**126**(1998), 3417-3425 Request permission

## 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.## References

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## Additional Information

**H. R. Hughes**- Affiliation: Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901-4408
- MR Author ID: 268902
- Email: hrhughes@math.siu.edu
- Received by editor(s): February 3, 1997
- Received by editor(s) in revised form: March 27, 1997
- Communicated by: Stanley Sawyer
- © Copyright 1998 American Mathematical Society
- 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