Persistence, resetting, and first-passage times of an active Ornstein--Uhlenbeck particle
Abstract
We study the first-passage time statistics of an active Ornstein--Uhlenbeck particle on a finite one-dimensional interval with an absorbing boundary at one end and a reflecting boundary at the other, subject to stochastic resetting. In the weak-activity regime, we develop a perturbative solution of the Fokker--Planck equation and use a renewal framework to obtain analytical expressions for the first-passage-time distribution and its low-order moments. In the absence of resetting, activity can either increase or decrease the mean first-passage time, depending on the relation between the persistence time and the diffusive time to absorption. When resetting is introduced, we determine both the onset of beneficial resetting and the finite range of resetting rates for which resetting lowers the mean first-passage time of the active system. We further show that the resetting transition depends on the velocity resetting protocol. Finally, by comparing the active particle with resetting to the passive Brownian particle without resetting, we construct a phase diagram that identifies the regions of parameter space in which activity and resetting together reduce the mean first-passage time.
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BibTeX
@misc{georgiou2026persistence,
title = {{Persistence, resetting, and first-passage times of an active Ornstein--Uhlenbeck particle}},
author = {Demosthenes K. Georgiou and Paul C. Bressloff and Thibault Bertrand},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21124},
eprint = {2609.21124},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21124},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Persistence, resetting, and first-passage times of an active Ornstein--Uhlenbeck particle
AU - Demosthenes K. Georgiou
AU - Paul C. Bressloff
AU - Thibault Bertrand
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.21124
UR - https://arxiv.org/abs/2609.21124
AB - We study the first-passage time statistics of an active Ornstein--Uhlenbeck particle on a finite one-dimensional interval with an absorbing boundary at one end and a reflecting boundary at the other, subject to stochastic resetting. In the weak-activity regime, we develop a perturbative solution of the Fokker--Planck equation and use a renewal framework to obtain analytical expressions for the first-passage-time distribution and its low-order moments. In the absence of resetting, activity can either increase or decrease the mean first-passage time, depending on the relation between the persistence time and the diffusive time to absorption. When resetting is introduced, we determine both the onset of beneficial resetting and the finite range of resetting rates for which resetting lowers the mean first-passage time of the active system. We further show that the resetting transition depends on the velocity resetting protocol. Finally, by comparing the active particle with resetting to the passive Brownian particle without resetting, we construct a phase diagram that identifies the regions of parameter space in which activity and resetting together reduce the mean first-passage time.
ER -