Scaling limits for random fields with long-range dependence

Ingemar Kaj, Lasse Leskelä, Ilkka Norros, Volker Schmidt

Research output: Contribution to journalArticleScientificpeer-review

24 Citations (Scopus)

Abstract

This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density λ of the sets grows to infinity and the mean volume ρ 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 λ and ρ are scaled.
If λ grows much faster than ρ 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
JournalAnnals of Probability
Volume35
Issue number2
DOIs
Publication statusPublished - 2007
MoE publication typeA1 Journal article-refereed

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Long-range Dependence
Scaling Limit
Random Field
Infinite Variance
Random Sets
Tail
Limiting
Infinity
Scaling
Tend
Moment
Long-range dependence
Random field
Zero

Cite this

Kaj, Ingemar ; Leskelä, Lasse ; Norros, Ilkka ; Schmidt, Volker. / Scaling limits for random fields with long-range dependence. In: Annals of Probability. 2007 ; Vol. 35, No. 2. pp. 528-550.
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Kaj, I, Leskelä, L, Norros, I & Schmidt, V 2007, 'Scaling limits for random fields with long-range dependence', Annals of Probability, vol. 35, no. 2, pp. 528-550. https://doi.org/10.1214/009117906000000700

Scaling limits for random fields with long-range dependence. / Kaj, Ingemar; Leskelä, Lasse; Norros, Ilkka; Schmidt, Volker.

In: Annals of Probability, Vol. 35, No. 2, 2007, p. 528-550.

Research output: Contribution to journalArticleScientificpeer-review

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