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dc.contributor.authorOwada, Takashi
dc.contributor.authorSamorodnitsky, Gennady
dc.description.abstractWe establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying Levy measures. The limit process is a new class of symmetric stable self-similar processes with stationary increments, that coincides on a part of its parameter space with a previously described process. The normalizing sequence and the limiting process are determined by the ergodic theoretical properties of the flow underlying the integral representation of the process. These properties can be interpreted as determining how long is the memory of the stationary infinitely divisible process. We also establish functional convergence, in a strong distributional sense, for conservative pointwise dual ergodic maps preserving an infinite measure.en_US
dc.description.sponsorshipARO grants W911NF-07-1-0078 and W911NF-12-10385, NSF grant DMS-1005903 and NSA grant H98230-11-1-0154en_US
dc.subjectinfinitely divisible processen_US
dc.subjectconservative flowen_US
dc.subjectcentral limit theoremen_US
dc.subjectself-similar processen_US
dc.subjectpointwise dual ergodicityen_US
dc.subjectDarling-Kac theoremen_US
dc.titleFunctional Central Limit Theorem for Heavy Tailed Stationary Infinitely Divisible Processes Generated by Conservative Flowsen_US
dc.typetechnical reporten_US

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