TY  - JOUR
A1  - Gairing, Jan
A1  - Högele, Michael
A1  - Kosenkova, Tetiana
T1  - Transportation distances and noise sensitivity of multiplicative Levy SDE with applications
JF  - Stochastic processes and their application
N2  - This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.
KW  - Stochastic differential equations
KW  - Multiplicative Levy noise
KW  - Levy type processes
KW  - Heavy-tailed distributions
KW  - Model selection
KW  - Wasserstein distance
KW  - Time series
Y1  - 2017
U6  - https://doi.org/10.1016/j.spa.2017.09.003
SN  - 0304-4149
SN  - 1879-209X
VL  - 128
IS  - 7
SP  - 2153
EP  - 2178
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Gairing, Jan
A1  - Högele, Michael
A1  - Kosenkova, Tetiana
A1  - Kulik, Alexei Michajlovič
T1  - Coupling distances between Levy measures and applications to noise sensitivity of SDE
JF  - Stochastics and dynamic
N2  - We introduce the notion of coupling distances on the space of Levy measures in order to quantify rates of convergence towards a limiting Levy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the Levy measure. The main result yields an estimate of the Wasserstein-Kantorovich-Rubinstein distance on path space between two Levy diffusions in terms of the coupling 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.
KW  - Levy diffusion approximation
KW  - coupling methods
KW  - principle
KW  - statistical model selection
Y1  - 2015
U6  - https://doi.org/10.1142/S0219493715500094
SN  - 0219-4937
SN  - 1793-6799
VL  - 15
IS  - 2
PB  - World Scientific
CY  - Singapore
ER  -