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Scaling limits for random fields with long-range dependence
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2007 (English)In: Annals of Probability, ISSN 0091-1798, Vol. 35, no 2, 528-550 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 35, no 2, 528-550 p.
Keyword [en]
long-range dependence, self-similar random field, fractional Brownian motion, fractional Gaussian noise, stable random measure, Riesz energy
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-77911DOI: 10.1214/009117906000000700ISI: 000245960600004OAI: oai:DiVA.org:uu-77911DiVA: diva2:105824
Available from: 2007-02-11 Created: 2007-02-11 Last updated: 2012-01-13

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Kaj, Ingemar

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