Large deviations and a Kramers' type law for self-stabilizing diffusions

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dc.creatorHerrmann, Samuel
dc.creatorImkeller, Peter
dc.creatorPeithmann, Dierk
dc.date2006-05-02
dc.date2008-08-26
dc.date.accessioned2026-07-07T09:58:46Z
dc.date.available2026-07-07T09:58:46Z
dc.descriptionWe 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AAP489 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0605053
dc.identifierhttp://arxiv.org/abs/math/0605053
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 4, 1379-1423
dc.identifierdoi:10.1214/07-AAP489
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167838
dc.subjectProbability
dc.subject60F10, 60H10 (Primary) 60K35, 37H10, 82C22 (Secondary)
dc.titleLarge deviations and a Kramers' type law for self-stabilizing diffusions
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