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Hitting times to spheres of Brownian motions with and without drifts


Authors: Yuji Hamana and Hiroyuki Matsumoto
Journal: Proc. Amer. Math. Soc. 144 (2016), 5385-5396
MSC (2010): Primary 60J65; Secondary 60J60, 60G40
DOI: https://doi.org/10.1090/proc/13136
Published electronically: June 3, 2016
MathSciNet review: 3556280
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Abstract: Explicit formulae for the densities of the first hitting times to the sphere of Brownian motions with drifts and the asymptotic behavior of the tail probabilities are shown. For this purpose we present an explicit formula for the Laplace transform of the joint distribution of the first hitting time to a sphere and the hitting position, which is different from the known formulae in the literature and is of independent interest.


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Additional Information

Yuji Hamana
Affiliation: Department of Mathematics, Kumamoto University, Kurokami 2-39-1, Kumamoto 860-8555, Japan
Email: hamana@kumamoto-u.ac.jp

Hiroyuki Matsumoto
Affiliation: Department of Physics and Mathematics, Aoyama Gakuin University, Fuchinobe 5-10-1, Sagamihara 252-5258, Japan
Email: matsu@gem.aoyama.ac.jp

DOI: https://doi.org/10.1090/proc/13136
Received by editor(s): April 28, 2015
Received by editor(s) in revised form: October 20, 2015, December 13, 2015, and February 4, 2016
Published electronically: June 3, 2016
Additional Notes: This work was partially supported by the Grant-in-Aid for Scientific Research (C) No.24540181 and No.26400144 of the Japan Society for the Promotion of Science (JSPS)
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2016 American Mathematical Society