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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
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