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December 1997 Extreme lengths in Brownian and Bessel excursions
Yueyun Hu, Zhan Shi
Bernoulli 3(4): 387-402 (December 1997).


We establish some strong limit theorems for the longest excursion lengths of a Bessel process of dimension d (0,2). In the special case d=1, we recover and improve some well-known results for Wiener processes, and solve an open problem raised. The proof relies on exact distributions evaluated by Pitman and Yor and on a careful analysis of the Bessel sample paths.


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Yueyun Hu. Zhan Shi. "Extreme lengths in Brownian and Bessel excursions." Bernoulli 3 (4) 387 - 402, December 1997.


Published: December 1997
First available in Project Euclid: 6 April 2007

zbMATH: 0907.60036
MathSciNet: MR1483694

Keywords: Bessel process , Brownian motion , excursion length , Lévy's class

Rights: Copyright © 1997 Bernoulli Society for Mathematical Statistics and Probability

Vol.3 • No. 4 • December 1997
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