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On generalized max-linear models in max-stable random fields
Michael Falk, Maximilian Zott · 2017-03-10 · via math.PR updates on arXiv.org

In practice, it is not possible to observe a whole max-stable random field. Therefore, a way how to reconstruct a max-stable random field in $C\left([0,1]^k\right)$ by interpolating its realizations at finitely many points is proposed. The resulting interpolating process is again a max-stable random field. This approach uses a \emph{generalized max-linear model}. Promising results have been established in the case $k=1$ in a previous paper. However, the extension to higher dimensions is not straightforward since we lose the natural order of the index space.

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