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dc.contributor.authorNickl, Richarden_US
dc.contributor.authorReiß, Markusen_US
dc.date.accessioned2012-01-06en_US
dc.date.accessioned2012-04-05T16:12:07Z-
dc.date.available2012-04-05T16:12:07Z-
dc.date.issued2012en_US
dc.identifier.urihttp://hdl.handle.net/10419/56623-
dc.description.abstractGiven n equidistant realisations of a Lévy process (Lt; t >= 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator. The class of Lévy processes covered includes several relevant examples such as compound Poisson, Gamma and self-decomposable processes. Main ideas in the proof include establishing pseudo-locality of the Fourier-integral operator and recent techniques from smoothed empirical processes.en_US
dc.language.isoengen_US
dc.publisherSFB 649, Economic Risk Berlinen_US
dc.relation.ispartofseriesSFB 649 discussion paper 2012-003en_US
dc.subject.jelC14en_US
dc.subject.jelC22en_US
dc.subject.ddc330en_US
dc.subject.keyworduniform central limit theoremen_US
dc.subject.keywordnonlinear inverse problemen_US
dc.subject.keywordsmoothed empirical processesen_US
dc.subject.keywordpseudo-differential operatorsen_US
dc.subject.keywordjump measureen_US
dc.subject.stwStochastischer Prozessen_US
dc.subject.stwSchätztheorieen_US
dc.subject.stwTheorieen_US
dc.titleA Donsker theorem for Lévy measuresen_US
dc.typeWorking Paperen_US
dc.identifier.ppn682401943en_US
dc.rightshttp://www.econstor.eu/dspace/Nutzungsbedingungenen_US
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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