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  - 
TY  - INPR
A1  - Gairing, Jan
A1  - Högele, Michael
A1  - Kosenkova, Tetiana
A1  - Kulik, Alexei Michajlovič
T1  - Coupling distances between Lévy measures and applications to noise sensitivity of SDE
N2  - We introduce the notion of coupling distances on the space of Lévy measures in order to quantify rates of convergence towards a limiting Lévy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the Lévy measure. The main result yields an estimate of the Wasserstein-Kantorovich-Rubinstein distance on path space between two Lévy diffusions in terms of the couping distances. We want to apply this to obtain precise rates of convergence for Markov chain approximations and a statistical goodness-of-fit test for low-dimensional conceptual climate models with paleoclimatic data.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)16 
KW  - Lévy diffusion approximation
KW  - coupling methods
KW  - Skorokhod' s invariance principle
KW  - statistical model selection
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68886
ER  - 
TY  - INPR
A1  - Debussche, Arnaud
A1  - Högele, Michael
A1  - Imkeller, Peter
T1  - The dynamics of nonlinear reaction-diffusion equations with small levy noise
T2  - Lecture notes in mathematics : a collection of informal reports and seminars
T2  - Lecture Notes in Mathematics
N2  - Our primary interest in this book lies in the study of dynamical properties of reaction-diffusion equations perturbed by Lévy noise of intensity ? in the small noise limit ??0 .
Y1  - 2013
SN  - 978-3-319-00828-8; 978-3-319-00827-1
U6  - https://doi.org/10.1007/978-3-319-00828-8_1
SN  - 0075-8434
VL  - 2085
SP  - 1
EP  - 10
PB  - Springer
CY  - Berlin
ER  -