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
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by Yuji Hamana and Hiroyuki Matsumoto PDF

Proc. Amer. Math. Soc. 144 (2016), 5385-5396 Request permission

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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