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dc.contributor.authorPipiras, Vladasen_US
dc.contributor.authorTaqqu, Murad S.en_US
dc.date.accessioned2019-08-28T14:08:38Z
dc.date.available2019-08-28T14:08:38Z
dc.date.issued2008-08-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000258633000002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationVladas Pipiras, Murad S Taqqu. 2008. "Identification of periodic and cyclic fractional stable motions." ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, Volume 44, Issue 4, pp. 612 - 637 (26). https://doi.org/10.1214/07-AIHP139
dc.identifier.issn0246-0203
dc.identifier.urihttps://hdl.handle.net/2144/37433
dc.description.abstractWe consider an important subclass of self-similar, non-Gaussian stable processes with stationary increments known as self-similar stable mixed moving averages. As previously shown by the authors, following the seminal approach of Jan Rosiński, these processes can be related to nonsingular flows through their minimal representations. Different types of flows give rise to different classes of self-similar mixed moving averages, and to corresponding general decompositions of these processes. Self-similar stable mixed moving averages related to dissipative flows have already been studied, as well as processes associated with identity flows which are the simplest type of conservative flows. The focus here is on self-similar stable mixed moving averages related to periodic and cyclic flows. Periodic flows are conservative flows such that each point in the space comes back to its initial position in finite time, either positive or null. The flow is cyclic if the return time is positive. Self-similar mixed moving averages are called periodic, resp. cyclic, fractional stable motions if their minimal representations are generated by periodic, resp. cyclic, flows. In practice, however, minimal representations are not particularly easy to determine and, moreover, self-similar stable mixed moving averages are often defined by nonminimal representations. We therefore provide a way which is not based on flows, to detect whether these processes are periodic or cyclic even if their representations are nonminimal. These identification results lead naturally to a decomposition of self-similar stable mixed moving averages which includes the new classes of periodic and cyclic fractional stable motions, and hence is more refined than the one previously established.en_US
dc.format.extent612 - 637 (26)en_US
dc.languageEnglish
dc.publisherGAUTHIER-VILLARS/EDITIONS ELSEVIERen_US
dc.relation.ispartofANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
dc.subjectStatistics & probabilityen_US
dc.subjectMathematicsen_US
dc.subjectSelf-similar processes with stationary incrementsen_US
dc.subjectMixed moving averagesen_US
dc.subjectDissipative and conservative flowsen_US
dc.subjectPeriodic and cyclic flowsen_US
dc.subjectPeriodic and cyclic fractional stable motionsen_US
dc.subjectStatisticsen_US
dc.titleIdentification of periodic and cyclic fractional stable motionsen_US
dc.typeArticleen_US
dc.description.versionFirst author draften_US
dc.identifier.doi10.1214/07-AIHP139
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.mycv54241


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