Generalized Pickands constants and stationary max-stable processes
Details
Download: R2.Extremes_PickandsConstant_Vers_UNIL.pdf (392.61 [Ko])
State: Public
Version: author
State: Public
Version: author
Serval ID
serval:BIB_9760DCC13F00
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Generalized Pickands constants and stationary max-stable processes
Journal
Extremes
ISSN
1386-1999
1572-915X
1572-915X
Publication state
Published
Issued date
09/2017
Peer-reviewed
Oui
Volume
20
Number
3
Pages
493-517
Language
english
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.
Keywords
Statistics and Probability, Engineering (miscellaneous), Economics, Econometrics and Finance (miscellaneous), Statistics and Probability, Engineering (miscellaneous), Economics, Econometrics and Finance (miscellaneous)
Create date
11/03/2017 11:58
Last modification date
20/08/2019 14:59