Renewal series and square-root boundaries for Bessel processes

Details Renewal series and square-root boundaries for Bessel processes Renewal series and square-root boundaries for Bessel processes

2008-06-19

arxiv.org/abs/0806.3197v1

Mathematics

Probability

Scientific paper

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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