Representations of max-stable processes via exponential tilting

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Serval ID
serval:BIB_FA961B329180
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Representations of max-stable processes via exponential tilting
Journal
Stochastic Processes and their Applications
Author(s)
Hashorva E.
ISSN
0304-4149
Publication state
Published
Issued date
09/2018
Peer-reviewed
Oui
Volume
128
Number
9
Pages
2952-2978
Language
english
Abstract
The recent contribution Dieker & Mikosch (2015) [1] obtained important representations of max-stable stationary Brown-Resnick random fields ζZ with a spectral representation determined by a Gaussian process Z. With motivations from \cite{DM} we derive for some general Z, representations for ζZ via exponential tilting of Z. Our main findings concern a) Dieker-Mikosch representations of max-stable processes, b) two-sided extensions of stationary max-stable processes, c) inf-argmax representation of any max-stable distribution, and d) new formulas for generalised Pickands constants. Our applications include new conditions for the stationarity of ζZ, a characterisation of Gaussian random vectors and an alternative proof of Kabluchko's characterisation of Gaussian processes with stationary increments.
Keywords
Modelling and Simulation, Statistics and Probability, Applied Mathematics
Create date
22/10/2017 17:38
Last modification date
20/08/2019 17:26
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