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Extreme value theory for long-range-dependent stable random fields. (English) Zbl 1477.60079

The authors introduce a class of symmetric stable random fields with long-range dependence. These are of the form \(\mathbf{X(n)}=\int_{E}f\circ T^{\mathbf{n}}(x)M(d\mathbf{x})\), \(\mathbf{n}\in \mathbb Z^{d}\), where \(T\) is a shift operator and \(M\) is a random measure with control measure \(\mu \) which satisfies among others some regularly varying conditions. The authors prove several functional extremal theorems in the space of sup measures and in the space of multivariate càdlàg functions. The resulting limits seem to be new and are related to the Fréchet distribution.

MSC:

60G60 Random fields
60G70 Extreme value theory; extremal stochastic processes
60G52 Stable stochastic processes

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References:

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