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Scaling limits for random fields with long-range dependence. (English) Zbl 1134.60027
The paper studies the possible limits of a spatial random field generated by uniformly scattered random sets, as the density \(\lambda\) of the sets grows to infinity and the mean volume \(\rho\) of the sets tends to zero. It is shown that the centrated and renormalized random field can have three different limits, depending on the relative speed at which \(\lambda\) and \(\rho\) are scaled.

MSC:
60F17 Functional limit theorems; invariance principles
60G60 Random fields
60G18 Self-similar stochastic processes
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