# Metastable behaviour of small noise Lévy-Driven diffusions

Peter Imkeller; Ilya Pavlyukevich

ESAIM: Probability and Statistics (2008)

- Volume: 12, page 412-437
- ISSN: 1292-8100

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topImkeller, Peter, and Pavlyukevich, Ilya. "Metastable behaviour of small noise Lévy-Driven diffusions." ESAIM: Probability and Statistics 12 (2008): 412-437. <http://eudml.org/doc/250429>.

@article{Imkeller2008,

abstract = {
We consider a dynamical system in $\mathbb\{R\}$ 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.
},

author = {Imkeller, Peter, Pavlyukevich, Ilya},

journal = {ESAIM: Probability and Statistics},

keywords = {Lévy process; jump diffusion; heavy tail; regular variation; metastability;
extreme events; first exit time; large deviations; extreme events},

language = {eng},

month = {7},

pages = {412-437},

publisher = {EDP Sciences},

title = {Metastable behaviour of small noise Lévy-Driven diffusions},

url = {http://eudml.org/doc/250429},

volume = {12},

year = {2008},

}

TY - JOUR

AU - Imkeller, Peter

AU - Pavlyukevich, Ilya

TI - Metastable behaviour of small noise Lévy-Driven diffusions

JO - ESAIM: Probability and Statistics

DA - 2008/7//

PB - EDP Sciences

VL - 12

SP - 412

EP - 437

AB -
We consider a dynamical system in $\mathbb{R}$ 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.

LA - eng

KW - Lévy process; jump diffusion; heavy tail; regular variation; metastability;
extreme events; first exit time; large deviations; extreme events

UR - http://eudml.org/doc/250429

ER -

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