Representations of Max-Stable Processes via Exponential Tilting

2016/05/10 by Hashorva, Enkelejd · 1 citation
#60G15 #60G70 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1605.03208

Abstract

The recent contribution Dieker & Mikosch (2015) [1] obtained important representations of max-stable stationary Brown-Resnick random fields ζ_Z with a spectral representation determined by a Gaussian process Z. With motivations from \citeDM we derive for some general Z, representations for ζ_Z 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 ζ_Z, a characterisation of Gaussian random vectors and an alternative proof of Kabluchko's characterisation of Gaussian processes with stationary increments.

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