Representations of max-stable processes via exponential tilting

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.