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2008 Renewal series and square-root boundaries for Bessel processes
Nathanael Enriquez, Christophe Sabot, Marc Yor
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Electron. Commun. Probab. 13: 649-652 (2008). DOI: 10.1214/ECP.v13-1436


We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical results by Breiman and Shepp, concerning Brownian motion, and recovers by different means, extensions for Bessel processes, obtained independently by Delong and Yor.


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Nathanael Enriquez. Christophe Sabot. Marc Yor. "Renewal series and square-root boundaries for Bessel processes." Electron. Commun. Probab. 13 649 - 652, 2008.


Accepted: 17 December 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1190.60031
MathSciNet: MR2466192
Digital Object Identifier: 10.1214/ECP.v13-1436

Primary: 60G40
Secondary: 60J57

Keywords: Bessel processes , Exponential functionals , renewal series , square-root boundaries

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