METASTABLE BEHAVIOUR OF SMALL NOISE LÉVY-DRIVEN DIFFUSIONS

@article{Imkeller2006METASTABLEBO,
  title={METASTABLE BEHAVIOUR OF SMALL NOISE L{\'E}VY-DRIVEN DIFFUSIONS},
  author={Peter Imkeller and Ilya Pavlyukevich},
  journal={Esaim: Probability and Statistics},
  year={2006},
  volume={12},
  pages={412-437}
}
We consider a dynamical system in R driven by a vector fieldU ,w hereU is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Levy noise of small intensity and such that the heaviest tail of its Levy 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… Expand
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