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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The probability distributions of the first hitting times of Bessel processes


Authors: Yuji Hamana and Hiroyuki Matsumoto
Journal: Trans. Amer. Math. Soc. 365 (2013), 5237-5257
MSC (2010): Primary 60J60; Secondary 33C10, 44A10
Published electronically: March 5, 2013
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Abstract: We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions by means of the zeros of the Bessel functions. The resulting formula is simpler and easier to treat than the corresponding results which have already been obtained.


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Additional Information

Yuji Hamana
Affiliation: Department of Mathematics, Kumamoto University, Kurokami 2-39-1, Kumamoto, Japan 860-8555

Hiroyuki Matsumoto
Affiliation: Department of Physics and Mathematics, Aoyama Gakuin University, Fuchinobe 5-10-1, Sagamihara, Japan 252-5258

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05799-6
PII: S 0002-9947(2013)05799-6
Keywords: Bessel process, first hitting time, Bessel functions
Received by editor(s): June 30, 2011
Received by editor(s) in revised form: July 26, 2011, and January 24, 2012
Published electronically: March 5, 2013
Additional Notes: The authors were partially supported by the Grant-in-Aid for Scientific Research (C) No. 20540121 and 23540183, Japan Society for the Promotion of Science.
Article copyright: © Copyright 2013 American Mathematical Society