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- Title
Generalized Pickands constants and stationary max-stable processes.
- Authors
Dȩbicki, Krzysztof; Engelke, Sebastian; Hashorva, Enkelejd
- 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 (Bernoulli, 20(3), 1600-1619, 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 Lévy processes. We furthermore develop a link to 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.
- Subjects
STOCHASTIC processes; GAUSSIAN processes; BROWNIAN motion; PHYSICAL constants; EXTREME value theory
- Publication
Extremes, 2017, Vol 20, Issue 3, p493
- ISSN
1386-1999
- Publication type
Article
- DOI
10.1007/s10687-017-0289-1