Metastable Behaviour of Small Noise Levy-Driven Diffusions

Peter Imkeller; Ilya Pavlyukevich

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Metastable Behaviour of Small Noise Levy-Driven Diffusions

Peter Imkeller·Ilya Pavlyukevich

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Abstract

We consider a dynamical system in R driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Levy noise of small intensity and such that the heaviest tail of its Levy measure is regularly varying. We show that the perturbed dynamical system exhibits metastable behaviour i.e. on a proper time scale it reminds of a Markov jump process taking values in the local minima of the potential U. Due to the heavy-tail nature of the random perturbation, the results differ strongly from the well studied purely Gaussian case.

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Peter Imkeller, Ilya Pavlyukevich. 2006-07-20. Metastable Behaviour of Small Noise Levy-Driven Diffusions. https://arxiv.org/abs/math/0601771

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