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Representations of max-stable processes via exponential tilting

Enkelejd Hashorva

Stochastic Processes and their Applications, 2018, vol. 128, issue 9, 2952-2978

Abstract: The recent contribution (Dieker and Mikosch, 2015) obtained representations of max-stable stationary Brown–Resnick process ζZ(t),t∈Rd with spectral process Z being Gaussian. With motivations from Dieker and Mikosch (2015) we derive for general Z, representations for ζZ via exponential tilting of Z. Our findings concern Dieker–Mikosch representations of max-stable processes, two-sided extensions of stationary max-stable processes, inf-argmax representation of max-stable distributions, and new formulas for generalised Pickands constants. Our applications include conditions for the stationarity of ζZ, a characterisation of Gaussian distributions and an alternative proof of Kabluchko’s characterisation of Gaussian processes with stationary increments.

Keywords: Max-stable process; Spectral tail process; Brown–Resnick stationary; Dieker–Mikosch representation; Inf-argmax representation; Pickands constants; Tilt-shift formula; Extremal index (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:eee:spapps:v:128:y:2018:i:9:p:2952-2978