DOI: 10.1051/ps:2007051 www.esaim-ps.org METASTABLE BEHAVIOUR OF SMALL NOISE LÉVY-DRIVEN DIFFUSIONS

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 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