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dc.contributor.authorBai, Shuyangen_US
dc.contributor.authorTaqqu, Murad S.en_US
dc.date.accessioned2020-01-23T14:46:59Z
dc.date.available2020-01-23T14:46:59Z
dc.date.issued2017-03-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000398966500016&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationShuyang Bai, Murad S Taqqu. 2017. "BEHAVIOR OF THE GENERALIZED ROSENBLATT PROCESS AT EXTREME CRITICAL EXPONENT VALUES." ANNALS OF PROBABILITY, Volume 45, Issue 2, pp. 1278 - 1324 (47). https://doi.org/10.1214/15-AOP1087
dc.identifier.issn0091-1798
dc.identifier.urihttps://hdl.handle.net/2144/39148
dc.description.abstractThe generalized Rosenblatt process is obtained by replacing the single critical exponent characterizing the Rosenblatt process by two different exponents living in the interior of a triangular region. What happens to that generalized Rosenblatt process as these critical exponents approach the boundaries of the triangle? We show by two different methods that on each of the two symmetric boundaries, the limit is non-Gaussian. On the third boundary, the limit is Brownian motion. The rates of convergence to these boundaries are also given. The situation is particularly delicate as one approaches the corners of the triangle, because the limit process will depend on how these corners are approached. All limits are in the sense of weak convergence in C[0,1]. These limits cannot be strengthened to convergence in L2(Ω).en_US
dc.description.sponsorshipSupported in part by NSF Grants DMS-10-07616 and DMS-13-09009 at Boston University. (DMS-10-07616 - NSF at Boston University; DMS-13-09009 - NSF at Boston University)en_US
dc.format.extentp. 1278 - 1324en_US
dc.languageEnglish
dc.language.isoen_US
dc.publisherINST MATHEMATICAL STATISTICSen_US
dc.relation.ispartofANNALS OF PROBABILITY
dc.subjectScience & technologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectStatistics & probabilityen_US
dc.subjectMathematicsen_US
dc.subjectLong memoryen_US
dc.subjectSelf-similar processesen_US
dc.subjectGeneralized Rosenblatt processesen_US
dc.subjectMultiple stochastic integralsen_US
dc.subjectCentral limit-theoremsen_US
dc.subjectHermite processesen_US
dc.subjectRandom-variablesen_US
dc.subjectWiener chaosen_US
dc.subjectMomenten_US
dc.subjectConvergenceen_US
dc.subjectCumulantsen_US
dc.subjectFormsen_US
dc.subjectStatisticsen_US
dc.titleBehavior of the generalized Rosenblatt process at extreme critical exponent valuesen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1214/15-AOP1087
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0002-1145-9082 (Taqqu, Murad S)
dc.identifier.mycv119093


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