Renewal series and square-root boundaries for Bessel processesReport as inadecuate

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

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.

Keywords : square-root boundaries Bessel processes renewal series exponential functionals square-root boundaries.

Author: Nathanael Enriquez - Christophe Sabot - Marc Yor -



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