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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Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2018, 23 (107), 24 pp. 〈10.1214/18-EJP235〉
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https://hal.archives-ouvertes.fr/hal-01771965
Contributeur : Olivier Durieu <>
Soumis le : vendredi 12 octobre 2018 - 13:02:06
Dernière modification le : vendredi 23 novembre 2018 - 13:34:02

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Olivier Durieu, Yizao Wang. A family of random sup-measures with long-range dependence. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2018, 23 (107), 24 pp. 〈10.1214/18-EJP235〉. 〈hal-01771965v2〉

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