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
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
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