Volume 12, April 2008
|Page(s)||412 - 437|
|Published online||25 July 2008|
Metastable behaviour of small noise Lévy-Driven diffusions
Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25,
12489 Berlin, Germany; email@example.com; firstname.lastname@example.org
We consider a dynamical system in 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.
Mathematics Subject Classification: 60E07 / 60F10
Key words: Lévy process / jump diffusion / heavy tail / regular variation / metastability / extreme events / first exit time / large deviations
© EDP Sciences, SMAI, 2008
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