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Some new classes of stationary max-stable random fields

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  • Robert, Christian Y.

Abstract

We present two new classes of stationary max-stable random fields. For the first class, we use the spectral representation due to Schlather (2002) and assume that the stationary process used in the representation is proportional to a power of a max-stable random field. We derive the finite dimensional distributions, explain the relationship between distributions of both max-stable random fields and give sufficient conditions for the sample paths to be γ-Hölder continuous functions for some γ∈(0,1). For the second class, we consider a multiplicative factor model and a Poisson–Voronoï tessellation of Rd to construct new max-stable random fields. We provide explicit expressions for the pairwise distribution function.

Suggested Citation

  • Robert, Christian Y., 2013. "Some new classes of stationary max-stable random fields," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1496-1503.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:6:p:1496-1503
    DOI: 10.1016/j.spl.2013.02.017
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    1. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
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    4. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
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    Cited by:

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    2. Enkelejd Hashorva & Simone A. Padoan & Stefano Rizzelli, 2021. "Multivariate extremes over a random number of observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 845-880, September.

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