Electronic Communications in Probability

Renewal series and square-root boundaries for Bessel processes

Nathanael Enriquez, Christophe Sabot, and Marc Yor

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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.

Article information

Electron. Commun. Probab., Volume 13 (2008), paper no. 59, 649-652.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60J57: Multiplicative functionals

Bessel processes renewal series exponential functionals square-root boundaries

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Enriquez, Nathanael; Sabot, Christophe; Yor, Marc. Renewal series and square-root boundaries for Bessel processes. Electron. Commun. Probab. 13 (2008), paper no. 59, 649--652. doi:10.1214/ECP.v13-1436. https://projecteuclid.org/euclid.ecp/1465233486

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