Electronic Communications in Probability

Renewal series and square-root boundaries for Bessel processes

Nathanael Enriquez, Christophe Sabot, and Marc Yor

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233486

Digital Object Identifier
doi:10.1214/ECP.v13-1436

Mathematical Reviews number (MathSciNet)
MR2466192

Zentralblatt MATH identifier
1190.60031

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

Keywords
Bessel processes renewal series exponential functionals square-root boundaries

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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References

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