@article{HoegelePavlyukevich2014,
  author    = {Hoegele, Michael and Pavlyukevich, Ilya},
  title     = {The exit problem from a neighborhood of the global attractor for dynamical systems perturbed by heavy-tailed levy processes},
  series = {Stochastic analysis and applications},
  volume    = {32},
  journal   = {Stochastic analysis and applications},
  number    = {1},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {0736-2994},
  doi       = {10.1080/07362994.2014.858554},
  pages     = {163 -- 190},
  year      = {2014},
  abstract  = {We consider a finite-dimensional deterministic dynamical system with the global attractor ? which supports a unique ergodic probability measure P. The measure P can be considered as the uniform long-term mean of the trajectories staying in a bounded domain D containing ?. We perturb the dynamical system by a multiplicative heavy tailed Levy noise of small intensity E>0 and solve the asymptotic first exit time and location problem from D in the limit of E?0. In contrast to the case of Gaussian perturbations, the exit time has an algebraic exit rate as a function of E, just as in the case when ? is a stable fixed point studied earlier in [9, 14, 19, 26]. As an example, we study the first exit problem from a neighborhood of the stable limit cycle for the Van der Pol oscillator perturbed by multiplicative -stable Levy noise.},
  language  = {en}
}