## Electronic Journal of Probability

### 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.

#### Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 107, 24 pp.

Dates
Accepted: 10 October 2018
First available in Project Euclid: 23 October 2018

https://projecteuclid.org/euclid.ejp/1540260053

Digital Object Identifier
doi:10.1214/18-EJP235

Mathematical Reviews number (MathSciNet)
MR3870450

Zentralblatt MATH identifier
06970412

#### Citation

Durieu, Olivier; Wang, Yizao. A family of random sup-measures with long-range dependence. Electron. J. Probab. 23 (2018), paper no. 107, 24 pp. doi:10.1214/18-EJP235. https://projecteuclid.org/euclid.ejp/1540260053

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