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March 2007 Scaling limits for random fields with long-range dependence
Ingemar Kaj, Lasse Leskelä, Ilkka Norros, Volker Schmidt
Ann. Probab. 35(2): 528-550 (March 2007). DOI: 10.1214/009117906000000700


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.


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Ingemar Kaj. Lasse Leskelä. Ilkka Norros. Volker Schmidt. "Scaling limits for random fields with long-range dependence." Ann. Probab. 35 (2) 528 - 550, March 2007.


Published: March 2007
First available in Project Euclid: 30 March 2007

zbMATH: 1134.60027
MathSciNet: MR2308587
Digital Object Identifier: 10.1214/009117906000000700

Primary: 60F17
Secondary: 60G18 , 60G60

Keywords: fractional Brownian motion , fractional Gaussian noise , long-range dependence , Riesz energy , self-similar random field , stable random measure

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 2 • March 2007
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