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2005-11-02Buch DOI: 10.18452/2558
Delay differential equations driven by Lévy processes: stationarity and Feller properties
dc.contributor.authorReiß, Markus
dc.contributor.authorRiedle, Markus
dc.contributor.authorGaans, Onno van
dc.date.accessioned2017-06-15T17:32:55Z
dc.date.available2017-06-15T17:32:55Z
dc.date.created2005-11-02
dc.date.issued2005-11-02
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3210
dc.description.abstractWe consider a stochastic delay differential equation driven by a general Lévy process. Both, the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment process is eventually Feller, but in general not eventually strong Feller on the Skorokhod space. The existence of an invariant measure is shown by proving tightness of the segments using semimartingale characteristics and the Krylov-Bogoliubov method. A counterexample shows that the stationary solution in completely general situations may not be unique, but in more specific cases uniqueness is established.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.subjectStochastic integral equationseng
dc.subjectGeneralizations of martingaleseng
dc.subjectStochastic delay equationseng
dc.subjectStochastic ordinary differential equationseng
dc.subjectStochastic stabilityeng
dc.subject.ddc510 Mathematik
dc.titleDelay differential equations driven by Lévy processes: stationarity and Feller properties
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10051785
dc.identifier.doihttp://dx.doi.org/10.18452/2558
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.pages28
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2005
local.edoc.container-issue6
local.edoc.container-year2005
local.edoc.container-erstkatid2075199-0

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