Semantic Apparatus – Independent factorization of the last zero arcsine law for Bessel processes with drift

Cited by Lee Sonogan

PPT - BESSEL'S EQUATION AND BESSEL FUNCTIONS : PowerPoint Presentation -  ID:1759692

Abstract by Hugo Panzo

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.

Publication: Project eucid (Peer-Reviewed Journal)

Pub Date: 2021: Doi: 10.1214/21-ECP405

https://projecteuclid.org/journals/electronic-communications-in-probability/volume-26/issue-none/Independent-factorization-of-the-last-zero-arcsine-law-for-Bessel/10.1214/21-ECP405.full (Plenty more sections and references in this research article)

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