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Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications

  • 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.

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Metadaten
Author:Jan Gairing, Michael HögeleGND, Tetiana Kosenkova
URN:urn:nbn:de:kobv:517-opus4-86693
ISSN:2193-6943 (online)
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (5 (2016) 2)
Publisher:Universitätsverlag Potsdam
Place of publication:Potsdam
Document Type:Preprint
Language:English
Year of first Publication:2016
Year of Completion:2016
Publishing Institution:Universität Potsdam
Publishing Institution:Universitätsverlag Potsdam
Release Date:2016/01/25
Tag:Lévy type processes; Wasserstein distance; heavy-tailed distributions; model selection; multiplicative Lévy noise; stochastic differential equations; time series
Volume:5
Issue:2
Pagenumber:24
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal 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) / 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) / 60Gxx Stochastic processes / 60G52 Stable 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) / 60Jxx Markov processes / 60J75 Jump processes
62-XX STATISTICS / 62Mxx Inference from stochastic processes / 62M10 Time series, auto-correlation, regression, etc. [See also 91B84]
Publication Way:Universitätsverlag Potsdam
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2016
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht