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Models for stationary max-stable random fields. (English) Zbl 1035.60054
The max-stable process \(Z\) is the limit process of maxima of i.i.d. random fields (processes). The author considers different methods of generating stationary max-stable processes on \(R^d\). For example, the following theorem is proved: Let \(Y\) be a stationary process on \(R^d\) with \(\mu= E\max\{0,Y(0)\}\in(0,\infty)\) and let \(\Pi\) be a Poisson process on \((0,\infty)\) with the intensity measure \(d\Lambda(s)=\mu^{-1}s^{-2}ds\). Then \(Z(x)=\max_{s\in\Pi} sY_s(x), \) where \(Y_s\) are i.i.d. copies of \(Y\), is a stationary max-stable process with unit Fréchet margins. A simulation technique for such processes is described.

MSC:
60G70 Extreme value theory; extremal stochastic processes
60G15 Gaussian processes
60G60 Random fields
Software:
R
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