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2021 Independent factorization of the last zero arcsine law for Bessel processes with drift
Hugo Panzo
Author Affiliations +
Electron. Commun. Probab. 26: 1-11 (2021). DOI: 10.1214/21-ECP405

Abstract

We show that the last zero before time t of a recurrent Bessel process with drift starting at 0 has the same distribution as the product of a right-censored exponential random variable and an independent beta random variable. This extends a recent result of Schulte-Geers and Stadje [19] from Brownian motion with drift to recurrent Bessel processes with drift. We give two proofs, one of which is intuitive, direct, and avoids heavy computations. For this we develop a novel additive decomposition for the square of a Bessel process with drift that may be of independent interest.

Funding Statement

Supported at the Technion by a Zuckerman Fellowship.

Acknowledgments

The author would like to thank Jim Pitman and Ernst Schulte-Geers for providing useful comments on earlier drafts and also thank an anonymous referee for pointing out formula (4.1) from Borodin and Salminen’s handbook [2].

Citation

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Hugo Panzo. "Independent factorization of the last zero arcsine law for Bessel processes with drift." Electron. Commun. Probab. 26 1 - 11, 2021. https://doi.org/10.1214/21-ECP405

Information

Received: 4 December 2020; Accepted: 27 May 2021; Published: 2021
First available in Project Euclid: 22 June 2021

Digital Object Identifier: 10.1214/21-ECP405

Subjects:
Primary: 60G17 , 60J60
Secondary: 60J65

Keywords: additivity property , arcsine law , Bessel bridge , Bessel process with drift , last exit time , time inversion property

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