Coupling distances between Lévy measures and applications to noise sensitivity of SDE

Gairing, Jan; Högele, Michael; Kosenkova, Tetiana; Kulik, Alexei Michajlovič

Coupling distances between Lévy measures and applications to noise sensitivity of SDE

Jan Gairing, Michael Högele, Tetiana Kosenkova, Alexei Michajlovič Kulik

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.

Metadaten
Author details:	Jan Gairing, Michael Högele GND, Tetiana Kosenkova, Alexei Michajlovič Kulik ORCiD GND
URN:	urn:nbn:de:kobv:517-opus-68886
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (2(2013)16)
Publication type:	Preprint
Language:	English
Publication year:	2013
Publishing institution:	Universität Potsdam
Release date:	2013/11/22
Tag:	Lévy diffusion approximation; Skorokhod' s invariance principle; coupling methods; statistical model selection
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Fxx Limit theorems [See also 28Dxx, 60B12] / 60F17 Functional limit theorems; invariance principles
	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G51 Processes with independent increments; Lévy processes
	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05]
	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J60 Diffusion processes [See also 58J65]
	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J75 Jump processes
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2013
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz

Coupling distances between Lévy measures and applications to noise sensitivity of SDE

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