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Self-similar Random Fields and Rescaled Random Balls Models
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2010 (English)In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 23, no 4, 1110-1141 p.Article in journal (Refereed) Published
Abstract [en]

We study generalized random fields which arise as rescaling limits of spatial configurations of uniformly scattered random balls as the mean radius of the balls tends to 0 or infinity. Assuming that the radius distribution has a power-law behavior, we prove that the centered and renormalized random balls field admits a limit with self-similarity properties. Our main result states that all self-similar, translation-and rotation-invariant Gaussian fields can be obtained through a unified zooming procedure starting from a random balls model. This approach has to be understood as a microscopic description of macroscopic properties. Under specific assumptions, we also get a Poisson-type asymptotic field. In addition to investigating stationarity and self-similarity properties, we give L-2-representations of the asymptotic generalized random fields viewed as continuous random linear functionals.

Place, publisher, year, edition, pages
2010. Vol. 23, no 4, 1110-1141 p.
Keyword [en]
Self-similarity, Generalized random field, Poisson point process, Fractional Poisson field, Fractional Brownian field
National Category
URN: urn:nbn:se:uu:diva-143664DOI: 10.1007/s10959-009-0259-xISI: 000285305200009OAI: oai:DiVA.org:uu-143664DiVA: diva2:390985
Available from: 2011-01-24 Created: 2011-01-24 Last updated: 2011-03-01Bibliographically approved

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