Self-similar random fields and rescaled random balls models

Abstract : 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, stationary and isotropic Gaussian fields. 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.
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https://hal.archives-ouvertes.fr/hal-00161614
Contributor : Hermine Biermé <>
Submitted on : Tuesday, February 12, 2008 - 5:05:39 PM
Last modification on : Friday, September 20, 2019 - 4:34:02 PM
Long-term archiving on: Tuesday, September 21, 2010 - 4:11:43 PM

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Hermine Biermé, Anne Estrade, Ingemar Kaj. Self-similar random fields and rescaled random balls models. Journal of theoretical probabability, 2010, 23 (4), pp.1110-1141. ⟨hal-00161614v2⟩

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