English

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

Probability 2018-10-11 v2

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.

Keywords

Cite

@article{arxiv.1804.07248,
  title  = {A family of random sup-measures with long-range dependence},
  author = {Olivier Durieu and Yizao Wang},
  journal= {arXiv preprint arXiv:1804.07248},
  year   = {2018}
}

Comments

23 pages; minor revision