Metastable behaviour of small noise Lévy-Driven diffusions
We consider a dynamical system in driven by a vector field -, where 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 on a proper time scale it reminds of a Markov jump process taking values in the local minima of the potential . Due to the heavy-tail nature of the...