The Annals of Probability
- Ann. Probab.
- Volume 35, Number 2 (2007), 528-550.
Scaling limits for random fields with long-range dependence
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.
Ann. Probab., Volume 35, Number 2 (2007), 528-550.
First available in Project Euclid: 30 March 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G60: Random fields 60G18: Self-similar processes
Kaj, Ingemar; Leskelä, Lasse; Norros, Ilkka; Schmidt, Volker. Scaling limits for random fields with long-range dependence. Ann. Probab. 35 (2007), no. 2, 528--550. doi:10.1214/009117906000000700. https://projecteuclid.org/euclid.aop/1175287753