Brownian hitting to spheres

Yuji Hamana; Hiroyuki Matsumoto

doi:10.2969/jmsj/91429142

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Brownian hitting to spheres

Yuji Hamana, Hiroyuki Matsumoto

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Keywords: Brownian motion, hitting times and places, spherical harmonics, one-dimensional diffusion

JOURNAL RESTRICTED ACCESS

2024 Volume 76 Issue 4 Pages 1307-1319

DOI https://doi.org/10.2969/jmsj/91429142

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Abstract

The joint distribution of the first hitting time of a Brownian motion with constant drift to a sphere and the hitting place is studied. Explicit formulae by means of spherical harmonics for the joint density are presented. The result is applied to a study on the asymptotic behavior of the distribution function.

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