HAL : hal-00139965, version 1

arXiv : math/0605053

DOI : 10.1214/07-AAP489

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

The Annals of Applied Probability 18, 4 (2008) 1379-1423

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

Samuel Herrmann 1, 2, Peter Imkeller, Dierk Peithmann

(2008)

We investigate exit times from domains of attraction for the motion of a self-stabilized particle travelling in a geometric (potential type) landscape and perturbed by Brownian noise of small amplitude. Self-stabilization is mediated by an ensemble-average attraction adding on to the individual potential 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 with 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.

1 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
2 :	TOSCA (INRIA Sophia Antipolis / INRIA Lorraine / IECN)
	INRIA – CNRS : UMR7502 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)

Domaine

:

Mathématiques/Probabilités

hal-00139965, version 1

http://hal.archives-ouvertes.fr/hal-00139965

oai:hal.archives-ouvertes.fr:hal-00139965

Contributeur : Samuel Herrmann <>

Soumis le : Mercredi 4 Avril 2007, 11:01:22

Dernière modification le : Vendredi 29 Avril 2011, 11:10:23