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Asymptotics of the densities of the first passage time distributions for Bessel diffusions


Author: Kôhei Uchiyama
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
Published electronically: September 4, 2014
MathSciNet review: 3301879
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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

DOI: https://doi.org/10.1090/S0002-9947-2014-06155-2
Keywords: First passage time, exterior problem, uniform estimate, Bessel diffusion
Received by editor(s): August 3, 2012
Received by editor(s) in revised form: March 11, 2013
Published electronically: September 4, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.