Scaling limits for random fields with long-range dependence

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

Research output: Contribution to journalArticleAcademicpeer-review

29 Citations (Scopus)
113 Downloads (Pure)


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
Issue number2
Publication statusPublished - 2007


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