@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}
}
@unpublished{HoegeleRuffino2013,
  author    = {H{\"o}gele, Michael and Ruffino, Paulo},
  title     = {Averaging along L{\´e}vy diffusions in foliated spaces},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64926},
  year      = {2013},
  abstract  = {We consider an SDE driven by a L{\´e}vy noise on a foliated manifold, whose trajectories stay on compact leaves. We determine the effective behavior of the system subject to a small smooth transversal perturbation of positive order epsilon. More precisely, we show that the average of the transversal component of the SDE converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to the invariant measures on the leaves (of the unpertubed system) as epsilon goes to 0. In particular we give upper bounds for the rates of convergence. The main results which are proved for pure jump L{\´e}vy processes complement the result by Gargate and Ruffino for Stratonovich SDEs to L{\´e}vy driven SDEs of Marcus type.},
  language  = {en}
}