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

Olivier Durieu (1) , Yizao Wang (2)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 Department of Mathematical Sciences [Cincinnati]

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.

Domaines: Probabilités [math.PR]

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