PreprintCC BY 4.0HAL
On the simultaneous zeroes of Bessel processes
Abstract
Given n independent squared Bessel processes, a priori with different dimensions, we investigate the first time ζ at which at least n -1 of them vanish simultaneously. We show that the tail asymptotics of ζ admits a power decay, with a persistence exponent given as the first positive pole of some explicit meromorphic function. This answers a question raised by Q. Berger, L. Béthencourt and C. Tardif in the case n = 3. We also provide along the way a closed-form expression for the Mellin transform of the position of the remaining process at time ζ. The paper is concluded by a more detailed study of the case of identical dimensions.
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BibTeX
@misc{profeta2026simultaneous,
title = {{On the simultaneous zeroes of Bessel processes}},
author = {Christophe Profeta},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25990},
eprint = {2610.25990},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05800955v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the simultaneous zeroes of Bessel processes
AU - Christophe Profeta
PY - 2026
DA - 2026/10/15
PB - HAL
DO - 10.48550/arxiv.2610.25990
UR - https://hal.science/hal-05800955v1
AB - Given n independent squared Bessel processes, a priori with different dimensions, we investigate the first time ζ at which at least n -1 of them vanish simultaneously. We show that the tail asymptotics of ζ admits a power decay, with a persistence exponent given as the first positive pole of some explicit meromorphic function. This answers a question raised by Q. Berger, L. Béthencourt and C. Tardif in the case n = 3. We also provide along the way a closed-form expression for the Mellin transform of the position of the remaining process at time ζ. The paper is concluded by a more detailed study of the case of identical dimensions.
ER -