TY  - INPR
A1  - Högele, Michael
A1  - Ruffino, Paulo
T1  - Averaging along Lévy diffusions in foliated spaces
N2  - We consider an SDE driven by a Lévy 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 Lévy processes complement the result by Gargate and Ruffino for Stratonovich SDEs to Lévy driven SDEs of Marcus type.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)10 
KW  - Averaging principle
KW  - foliated diffusion
KW  - Lévy diffusions on manifolds
KW  - canonical Marcus integration
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64926
SN  - 2193-6943
ER  -