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February, 1980 Hitting Spheres with Brownian Motion
J. G. Wendel
Ann. Probab. 8(1): 164-169 (February, 1980). DOI: 10.1214/aop/1176994833


Let $X_t$ be standard Brownian motion in $R^d$ starting at fixed $X_0$, and let $T$ be the hitting time for a sphere or concentric spherical shell. Explicit formulas, in terms of a natural Laplace-Gegenbauer transform, are obtained for the joint distribution of $T$ and $X_T$.


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J. G. Wendel. "Hitting Spheres with Brownian Motion." Ann. Probab. 8 (1) 164 - 169, February, 1980.


Published: February, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0426.60072
MathSciNet: MR556423
Digital Object Identifier: 10.1214/aop/1176994833

Primary: 60J65
Secondary: 33A40 , 33A45

Keywords: Brownian motion , hitting times and places , shells , spheres

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 1 • February, 1980
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