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Levy multiplicative chaos and star scale invariant random measures

dc.contributor.authorSohier, Julien
dc.contributor.authorVargas, Vincent
HAL ID: 739861
dc.contributor.authorRhodes, Rémi
dc.date.accessioned2012-02-07T12:43:39Z
dc.date.available2012-02-07T12:43:39Z
dc.date.issued2014
dc.identifier.issn0091-1798
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/8052
dc.language.isoenen
dc.subjectmultifractal processes
dc.subjectinfinitely divisible processes
dc.subjectmultiplicative chaos
dc.subjectuniqueness
dc.subject.ddc519en
dc.titleLevy multiplicative chaos and star scale invariant random measures
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this article, we consider the continuous analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation. We obtain an explicit characterization of the structure of these measures, which reflects the constraints imposed by the continuous setting. In particular, we show that the continuous equation enjoys some specific properties that do not appear in the discrete star equation. To that purpose, we define a Levy multiplicative chaos that generalizes the already existing constructions.
dc.relation.isversionofjnlnameAnnals of Probability
dc.relation.isversionofjnlvol42
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages689-724
dc.relation.isversionofdoihttp://dx.doi.org/10.1214/12-AOP810
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-00662375
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statistics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-10-27T11:56:55Z


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