• Corpus ID: 238856684

Phase transition for extremes of a family of stationary multiple-stable processes

@inproceedings{Bai2021PhaseTF,
  title={Phase transition for extremes of a family of stationary multiple-stable processes},
  author={Shuyang Bai and Yizao Wang},
  year={2021}
}

• Shuyang Bai, Yizao Wang
• Published 14 October 2021
• Mathematics

We investigate a family of stationary processes that may exhibit either long-range or short-range dependence, depending on the parameters. The processes can be represented as multiple stable integrals, and there are two parameters for the processes, the memory parameter β ∈ (0, 1) and the multiplicity parameter p ∈ N. We investigate the macroscopic limit of extremes of the process, in terms of convergence of random sup-measures, for the full range of parameters. Our results show that (i) the extremes of the process exhibit long-range dependence when βp := pβ − p + 1 ∈ (0, 1), with a new family of random sup-measures arising in the limit, (ii) the extremes are of short-range dependence when βp < 0, with independently scattered random sup-measures arising in the limit, and (iii) there is a delicate phase transition at the critical regime βp = 0.