TY  - INPR
A1  - Gairing, Jan
A1  - Högele, Michael
A1  - Kosenkova, Tetiana
T1  - Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications
N2  - This article assesses the distance between the laws of stochastic differential equations with multiplicative Lévy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Lévy 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 2 
KW  - stochastic differential equations
KW  - multiplicative Lévy noise
KW  - Lévy type processes
KW  - heavy-tailed distributions
KW  - model selection
KW  - Wasserstein distance
KW  - time series
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-86693
SN  - 2193-6943
VL  - 5
IS  - 2
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Gairing, Jan
A1  - Högele, Michael
A1  - Kosenkova, Tetiana
A1  - Kulik, Alexei Michajlovič
T1  - On the calibration of Lévy driven time series with coupling distances : an application in paleoclimate
N2  - This article aims at the statistical assessment of time series with large fluctuations in short time, which are assumed to stem from a continuous process perturbed by a Lévy process exhibiting a heavy tail behavior. We propose an easily implementable procedure to estimate efficiently the statistical difference between the noisy behavior of the data and a given reference jump measure in terms of so-called coupling distances. After a short introduction to Lévy processes and coupling distances we recall basic statistical approximation results and derive rates of convergence. In the sequel the procedure is elaborated in detail in an abstract setting and eventually applied in a case study to simulated and paleoclimate data. It indicates the dominant presence of a non-stable heavy-tailed jump Lévy component for some tail index greater than 2.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 2 
KW  - time series with heavy tails
KW  - index of stability
KW  - goodness-of-fit
KW  - empirical Wasserstein distance
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-69781
SN  - 2193-6943
VL  - 3
IS  - 2
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  -