Scaling limits for random fields with long-range dependence

I. Kaj, L. Leskelä, I. Norros, V. Schmidt

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    26 Citations (Scopus)
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    Abstract

    This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density ¿ of the sets grows to infinity and the mean volume ¿ of the sets tends to zero. Assuming that the volume distribution has a regularly varying tail with infinite variance, we show that the centered and renormalized random field can have three different limits, depending on the relative speed at which ¿ and ¿ are scaled. If ¿ grows much faster than ¿ shrinks, the limit is Gaussian with long-range dependence, while in the opposite case, the limit is independently scattered with infinite second moments. In a special intermediate scaling regime, there exists a nontrivial limiting random field that is not stable.
    Original languageEnglish
    Pages (from-to)528-550
    JournalThe Annals of Probability
    Volume35
    Issue number2
    DOIs
    Publication statusPublished - 2007

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