serval:BIB_FA961B329180
Representations of max-stable processes via exponential tilting
10.1016/j.spa.2017.10.003
Hashorva
E.
author
article
2018-09
Stochastic Processes and their Applications
0304-4149
journal
128
9
2952-2978
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.
Modelling and Simulation
Statistics and Probability
Applied Mathematics
eng
60_published
peer-reviewed
University of Lausanne
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