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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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