Volume 24, 2020
|Page(s)||399 - 407|
|Published online||25 September 2020|
Exit-time of mean-field particles system
Univ Lyon, Université Jean Monnet, CNRS UMR 5208, Institut Camille Jordan, Maison de l’Université, 10 rue Tréfilerie, CS 82301,
Saint-Étienne Cedex 2, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 2 December 2019
The current article is devoted to the study of a mean-field system of particles. The question that we are interested in is the behaviour of the exit-time of the first particle (and the one of any particle) from a domain D on ℝd as the diffusion coefficient goes to 0. We establish a Kramers’ type law. In other words, we show that the exit-time is exponentially equivalent to , HN being the exit-cost. We also show that this exit-cost converges to some quantity H.
Mathematics Subject Classification: 60F10 / 60J60 / 60H10
Key words: Exit-problem / large deviations / interacting particle systems / mean-field systems
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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