Renewal series and square-root boundaries for Bessel processes

Nathanael Enriquez (1) , Christophe Sabot (2) , Marc Yor (3, 4)

1 MODAL'X - Modélisation aléatoire de Paris X
2 ICJ - Institut Camille Jordan
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 IUF - Institut universitaire de France

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.

Mots clés: Bessel processes; renewal series; exponential functionals; square-root boundaries.; square-root boundaries

Domaines: Probabilités [math.PR]

Nathanael Enriquez, Christophe Sabot, Marc Yor. Renewal series and square-root boundaries for Bessel processes. 2008. ⟨hal-00289151⟩