Renewal series and square-root boundaries for Bessel processes

Nathanael Enriquez; Christophe Sabot; Marc Yor

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arXiv · 0806.3197

Renewal series and square-root boundaries for Bessel processes

Nathanael Enriquez·Christophe Sabot·Marc Yor

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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.

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Nathanael Enriquez, Christophe Sabot, Marc Yor. 2008-06-19. Renewal series and square-root boundaries for Bessel processes. https://arxiv.org/abs/0806.3197

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