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Self-similar random fields and rescaled random balls models
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics. Matematisk statistik.
2007 (English)Report (Other scientific)
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 strong spatial

dependence. In particular, our approach provides a unified framework

to obtain all self-similar, translation and rotation

invariant Gaussian fields.

In addition to investigating stationarity and self-similarity

properties, we give $L2$-representations of the asymptotic generalized

random fields viewed as continuous random linear functionals.

Place, publisher, year, edition, pages
2007. , 26 p.
Series
Uppsala University Department of Mathematics Report Series, ISSN 1101-3591 ; 2007:30
Identifiers
URN: urn:nbn:se:uu:diva-14999OAI: oai:DiVA.org:uu-14999DiVA: diva2:42770
Available from: 2008-02-01 Created: 2008-02-01

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http://www.math.uu.se/~ikaj/papers/ssrfscaling.pdf
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