Generalized Pickands constants and stationary max-stable processes
Abstract
Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often unknown. Recently, Dieker and Yakir (2014) derived a novel representation of Pickands constant as a simple expected value that does not involve a limit operation. In this paper we show that the notion of Pickands constants and their corresponding Dieker-Yakir representations can be extended to a large class of stochastic processes, including general Gaussian and L\'evy processes. We furthermore provide a link to spatial extreme value theory and show that Pickands-type constants coincide with certain constants arising in the study of max-stable processes with mixed moving maxima representations.
Cite
@article{arxiv.1602.01613,
title = {Generalized Pickands constants and stationary max-stable processes},
author = {Krzysztof Dębicki and Sebastian Engelke and Enkelejd Hashorva},
journal= {arXiv preprint arXiv:1602.01613},
year = {2016}
}