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  - 
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  - Cattiaux, Patrick
A1  - Fradon, Myriam
A1  - Kulik, Alexei Michajlovič
A1  - Roelly, Sylvie
T1  - Long time behavior of stochastic hard ball systems
N2  - We study the long time behavior of a system of two or three Brownian hard balls living in the Euclidean space of dimension at least two, submitted to a mutual attraction and to elastic collisions.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)15 
KW  - Stochastic differential equations
KW  - hard core interaction
KW  - reversible measure
KW  - normal reflection
KW  - local time
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68388
ER  -