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

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

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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
Verfasserangaben:	Jan Gairing, Michael Högele GND, Tetiana Kosenkova, Alexei Michajlovič Kulik ORCiD GND
URN:	urn:nbn:de:kobv:517-opus-68886
Schriftenreihe (Bandnummer):	Preprints des Instituts für Mathematik der Universität Potsdam (2(2013)16)
Publikationstyp:	Preprint
Sprache:	Englisch
Erscheinungsjahr:	2013
Veröffentlichende Institution:	Universität Potsdam
Datum der Freischaltung:	22.11.2013
Freies Schlagwort / Tag:	Lévy diffusion approximation; Skorokhod' s invariance principle; coupling methods; statistical model selection
Organisationseinheiten:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC-Klassifikation:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Klassifikation:	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
Sammlung(en):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2013
Lizenz (Deutsch):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz

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

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