A pursuit problem for squared Bessel processes
Probability
2025-08-12 v2
Abstract
In this note, we are interested in the probability that two independent squared Bessel processes do not cross for a long time. We show that this probability has a power decay which is given by the first zero of some hypergeometric function. We also compute along the way the distribution of the location where the crossing eventually occurs.
Cite
@article{arxiv.2411.12315,
title = {A pursuit problem for squared Bessel processes},
author = {Christophe Profeta},
journal= {arXiv preprint arXiv:2411.12315},
year = {2025}
}