A unifying approach to fractional Lévy processes

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dc.contributor.authorEngelke, Sebastian
dc.contributor.authorWoerner, Jeannette H. C.
dc.date.accessioned2010-12-21T14:55:15Z
dc.date.available2010-12-21T14:55:15Z
dc.date.issued2010-12-21
dc.description.abstractStarting from the moving average representation of fractional Brownian motion fractional Lévy processes have been constructed by keeping the same moving average kernel and replacing the Brownian motion by a pure jump Lévy process with finite second moments. Another way was to replace the Brownian motion by an alpha-stable Lévy process and the exponent in the kernel by H-1/alpha. We now provide a unifying approach taking kernels of the form a((t-s)_+^gamma - (-s)_+^gamma) + b((t-s)_-^gamma - (-s)_-^gamma), where gamma can be chosen according to the existing moments and the Blumenthal-Getoor index of the underlying Lévy process. These processes may exhibit both long and short range dependence. In addition we will examine further properties of the processes, e.g. regularity of the sample paths and the semimartingale property. MSC 2010: 60G22, 60E07en
dc.identifier.urihttp://hdl.handle.net/2003/27542
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-7287
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB 823 ; 50/2010
dc.relation.isversionofhttp://hdl.handle.net/2003/27541
dc.subjectBlumenthal-Getoor indexen
dc.subjectCorrelationen
dc.subjectFractional Brownian motionen
dc.subjectFractional Lévy processen
dc.subjectLinear fractional stable motionen
dc.subjectLong-range dependenceen
dc.subjectSemimartingaleen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleA unifying approach to fractional Lévy processesen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

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