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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Asymptotics of the densities of the first passage time distributions for Bessel diffusions
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by Kôhei Uchiyama PDF
Trans. Amer. Math. Soc. 367 (2015), 2719-2742 Request permission

Abstract:

This paper concerns the first passage times to a point $a >0$, denoted by $\sigma _a$, of Bessel processes. We are interested in the case when the process starts at $x>a$ and we compute the densities of the distributions of $\sigma _a$ to obtain the exact asymptotic forms of them as $t\to \infty$ that are valid uniformly in $x>a$ for every order of the Bessel process.
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Additional Information
  • Kôhei Uchiyama
  • Affiliation: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro Tokyo 152-8551, Japan
  • Email: uchiyama@math.titech.ac.jp
  • Received by editor(s): August 3, 2012
  • Received by editor(s) in revised form: March 11, 2013
  • Published electronically: September 4, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 2719-2742
  • MSC (2010): Primary 60J65; Secondary 60J60
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06155-2
  • MathSciNet review: 3301879