Metastable behaviour of small noise Lévy-driven diffusions
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 412-437.

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.

DOI : 10.1051/ps:2007051
Classification : 60E07, 60F10
Mots-clés : Lévy process, jump diffusion, heavy tail, regular variation, metastability, extreme events, first exit time, large deviations 
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     title = {Metastable behaviour of small noise {L\'evy-driven} diffusions},
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Imkeller, Peter; Pavlyukevich, Ilya. Metastable behaviour of small noise Lévy-driven diffusions. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 412-437. doi : 10.1051/ps:2007051. http://www.numdam.org/articles/10.1051/ps:2007051/

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