Averaging principle for Lévy diffusions

In this talk we analise an averaging principle for Lévy diffusions which live on the leaves of a foliated
manifold subject to small transversal Léevy type perturbation to the case of non-compact leaves. The main
result states that the existence of p-th moments of the foliated Lévy diffusion for p > 2 and an ergodic
convergence of its coecients in Lp implies the strong Lp convergence of the fast perturbed motion on
the time scale t/ to the system driven by the averaged coeffcients.