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October, 1979 The Brownian Escape Process
R. K. Getoor
Ann. Probab. 7(5): 864-867 (October, 1979). DOI: 10.1214/aop/1176994945

Abstract

Let $X$ be the Brownian motion process in $\mathbb{R}^d, d \geqslant 3$ with $X(0) = 0$. Let $L_r$ be the last exit time of $X$ from the ball of radius $r$ centered at the origin. Then $(L_r)$ has independent increments and we compute the distribution of $L_r$. When $d = 3$ this yields a simple proof of a recent result of Pitman.

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R. K. Getoor. "The Brownian Escape Process." Ann. Probab. 7 (5) 864 - 867, October, 1979. https://doi.org/10.1214/aop/1176994945

Information

Published: October, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0416.60086
MathSciNet: MR542136
Digital Object Identifier: 10.1214/aop/1176994945

Subjects:
Primary: 60J65
Secondary: 60J30

Keywords: Brownian motion , Independent increments , Infinitely divisible , last exit

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 5 • October, 1979
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