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dc.contributor.authorSamorodnitskty, Gennady
dc.contributor.authorWang, Yizao
dc.date.accessioned2017-03-22T18:15:45Z
dc.date.available2017-03-22T18:15:45Z
dc.date.issued2017-03
dc.identifier.urihttps://hdl.handle.net/1813/47543
dc.description.abstractWe prove limit theorems of an entirely new type for certain long memory regularly varying stationary \id\ random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one regime, our results exhibit limits that are not among the classical extreme value distributions. Restricted to the one-dimensional case, the distributions we obtain interpolate, in the appropriate parameter range, the $\alpha$-Fr\'echet distribution and the skewed $\alpha$-stable distribution. In general, the limit is a new family of stationary and self-similar random sup-measures with parameters $\alpha\in(0,\infty)$ and $\beta\in(0,1)$, with representations based on intersections of independent $\beta$-stable regenerative sets. The tail of the limit random sup-measure on each interval with finite positive length is regularly varying with index $-\alpha$. The intriguing structure of these random sup-measures is due to intersections of independent $\beta$-stable regenerative sets and the fact that the number of such sets intersecting simultaneously increases to infinity as $\beta$ increases to one. The results in this paper extend substantially previous investigations where only $\alpha\in(0,2)$ and $\beta\in(0,1/2)$ have been considered.en_US
dc.description.sponsorshipSamorodnitsky's research was partially supported by the NSF grant DMS-1506783 and the ARO grant W911NF-12-10385 at Cornell University. Wang's research was partially supported by the NSA grants H98230-14-1-0318 and H98230-16-1-0322, and the ARO grant W911NF-17-1-0006 at University of Cincinnati.en_US
dc.language.isoen_USen_US
dc.subjectExtreme value theoryen_US
dc.subjectrandom sup-measureen_US
dc.subjectrandom upper-semi-continuous functionen_US
dc.subjectstationary infinitely divisible processen_US
dc.subjectlong range dependenceen_US
dc.titleExtremal theory for long range dependent infinitely divisible processesen_US
dc.typearticleen_US


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