We investigate exit times from domains of attraction for the motion of a self-stabilized particle traveling in a geometric (potential type) landscape and perturbed by Brownian noise of small amplitude. Self-stabilization is the effect of including an ensemble-average attraction in addition to the usual state-dependent drift, where the particle is supposed to be suspended in a large population of identical ones. A Kramers’ type law for the particle’s exit from the potential’s domains of attraction and a large deviations principle for the self-stabilizing diffusion are proved. It turns out that the exit law for the self-stabilizing diffusion coincides with the exit law of a potential diffusion without self-stabilization and a drift component perturbed by average attraction. We show that self-stabilization may substantially delay the exit from domains of attraction, and that the exit location may be completely different.
Publié le : 2008-08-15
Classification:
Self-stabilization,
diffusion,
exit time,
exit law,
large deviations,
interacting particle systems,
domain of attraction,
propagation of chaos,
60F10,
60H10,
60K35,
37H10,
82C22
@article{1216677126,
author = {Herrmann, Samuel and Imkeller, Peter and Peithmann, Dierk},
title = {Large deviations and a Kramers' type law for self-stabilizing diffusions},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 1379-1423},
language = {en},
url = {http://dml.mathdoc.fr/item/1216677126}
}
Herrmann, Samuel; Imkeller, Peter; Peithmann, Dierk. Large deviations and a Kramers’ type law for self-stabilizing diffusions. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 1379-1423. http://gdmltest.u-ga.fr/item/1216677126/