Representations of max-stable processes via exponential tilting |
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Authors: | Enkelejd Hashorva |
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Institution: | Department of Actuarial Science, University of Lausanne, Chamberonne, 1015 Lausanne, Switzerland |
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Abstract: | The recent contribution (Dieker and Mikosch, 2015) obtained representations of max-stable stationary Brown–Resnick process with spectral process being Gaussian. With motivations from Dieker and Mikosch (2015) we derive for general , representations for via exponential tilting of . 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 , a characterisation of Gaussian distributions and an alternative proof of Kabluchko’s characterisation of Gaussian processes with stationary increments. |
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Keywords: | primary 60G15 secondary 60G70 Max-stable process Spectral tail process Brown–Resnick stationary Dieker–Mikosch representation Inf-argmax representation Pickands constants Tilt-shift formula Extremal index |
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