A family of random sup-measures with long-range dependence

Abstract : A family of self-similar and translation-invariant random sup-measures with long-range dependence are investigated. They are shown to arise as the limit of the empirical random sup-measure of a stationary heavy-tailed process, inspired by an infinite urn scheme, where same values are repeated at several random locations. The random sup-measure reflects the long-range dependence nature of the original process, and in particular characterizes how locations of extremes appear as long-range clusters represented by random closed sets. A limit theorem for the corresponding point-process convergence is established.
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Pré-publication, Document de travail
22 pages. 2018
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https://hal.archives-ouvertes.fr/hal-01771965
Contributeur : Olivier Durieu <>
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Dernière modification le : mercredi 19 septembre 2018 - 11:42:03
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  • HAL Id : hal-01771965, version 1
  • ARXIV : 1804.07248

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Olivier Durieu, Yizao Wang. A family of random sup-measures with long-range dependence. 22 pages. 2018. 〈hal-01771965〉

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