Metastable behaviour of small noise Lévy-driven diffusions

Imkeller, Peter; Pavlyukevich, Ilya

ESAIM: Probability and Statistics, Tome 12 (2008), pp. 412-437.

We consider a dynamical system in $ℝ$ driven by a vector field $-U^{\text{'}}$, where $U$ is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Lévy noise of small intensity and such that the heaviest tail of its Lévy 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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