Abstract
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.
Citation
Samuel Herrmann. Peter Imkeller. Dierk Peithmann. "Large deviations and a Kramers’ type law for self-stabilizing diffusions." Ann. Appl. Probab. 18 (4) 1379 - 1423, August 2008. https://doi.org/10.1214/07-AAP489
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