@article{DebusscheHoegeleImkeller2013,
  author    = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter},
  title     = {The source of stochastic models in conceptual climate dynamics},
  series = {Lecture notes in mathematics : a collection of informal reports and seminars},
  volume    = {2085},
  journal   = {Lecture notes in mathematics : a collection of informal reports and seminars},
  number    = {3},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-319-00828-8; 978-3-319-00827-1},
  issn      = {0075-8434},
  doi       = {10.1007/978-3-319-00828-8},
  pages     = {151 -- 157},
  year      = {2013},
  language  = {en}
}
@article{DebusscheHoegeleImkeller2013,
  author    = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter},
  title     = {The small deviation of the small noise solution},
  series = {Lecture notes in mathematics : a collection of informal reports and seminars},
  volume    = {2085},
  journal   = {Lecture notes in mathematics : a collection of informal reports and seminars},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-319-00828-8; 978-3-319-00827-1},
  issn      = {0075-8434},
  doi       = {10.1007/978-3-319-00828-8_4},
  pages     = {69 -- 85},
  year      = {2013},
  language  = {en}
}
@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}
}
@article{HoegeleRuffino2015,
  author    = {Hoegele, Michael and Ruffino, Paulo},
  title     = {Averaging along foliated Levy diffusions},
  series = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  volume    = {112},
  journal   = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0362-546X},
  doi       = {10.1016/j.na.2014.09.006},
  pages     = {1 -- 14},
  year      = {2015},
  abstract  = {This article studies the dynamics of the strong solution of a SDE driven by a discontinuous Levy process taking values in a smooth foliated manifold with compact leaves. It is assumed that it is foliated in the sense that its trajectories stay on the leaf of their initial value for all times almost surely. Under a generic ergodicity assumption for each leaf, we determine the effective behaviour of the system subject to a small smooth perturbation of order epsilon > 0, which acts transversal to the leaves. The main result states that, on average, the transversal component of the perturbed SDE converges uniformly to the solution of a deterministic ODE as e tends to zero. This transversal ODE is generated by the average of the perturbing vector field with respect to the invariant measures of the unperturbed system and varies with the transversal height of the leaves. We give upper bounds for the rates of convergence and illustrate these results for the random rotations on the circle. This article complements the results by Gonzales and Ruffino for SDEs of Stratonovich type to general Levy driven SDEs of Marcus type.},
  language  = {en}
}
@article{DebusscheHoegeleImkeller2013,
  author    = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter},
  title     = {Asymptotic transition times},
  series = {Lecture notes in mathematics : a collection of informal reports and seminars},
  volume    = {2085},
  journal   = {Lecture notes in mathematics : a collection of informal reports and seminars},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-319-00828-8; 978-3-319-00827-1},
  issn      = {0075-8434},
  doi       = {10.1007/978-3-319-00828-8_6},
  pages     = {121 -- 130},
  year      = {2013},
  language  = {en}
}
@article{DebusscheHoegeleImkeller2013,
  author    = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter},
  title     = {Asymptotic exit times},
  series = {Lecture notes in mathematics : a collection of informal reports and seminars},
  volume    = {2085},
  journal   = {Lecture notes in mathematics : a collection of informal reports and seminars},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-319-00828-8; 978-3-319-00827-1},
  issn      = {0075-8434},
  doi       = {10.1007/978-3-319-00828-8_5},
  pages     = {87 -- 120},
  year      = {2013},
  language  = {en}
}