# 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} }

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…

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