Hitting times to spheres of Brownian motions with and without drifts

Hamana, Yuji; Matsumoto, Hiroyuki

doi:10.1090/proc/13136

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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