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Representations of max-stable processes via exponential tilting

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  • Hashorva, Enkelejd

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.

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  • Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:9:p:2952-2978
    DOI: 10.1016/j.spa.2017.10.003
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    References listed on IDEAS

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    1. Krzysztof Dȩbicki & Enkelejd Hashorva, 2020. "Approximation of Supremum of Max-Stable Stationary Processes & Pickands Constants," Journal of Theoretical Probability, Springer, vol. 33(1), pages 444-464, March.
    2. Bai, Long, 2020. "Extremes of standard multifractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 159(C).
    3. Krzysztof Dȩbicki & Zbigniew Michna & Xiaofan Peng, 2019. "Approximation of Sojourn Times of Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1183-1213, December.
    4. Hashorva, Enkelejd & Kume, Alfred, 2021. "Multivariate max-stable processes and homogeneous functionals," Statistics & Probability Letters, Elsevier, vol. 173(C).
    5. E. Hashorva, 2018. "Approximation of Some Multivariate Risk Measures for Gaussian Risks," Papers 1803.06922, arXiv.org, revised Oct 2018.

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