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Article Dans Une Revue Journal of Theoretical Probability Année : 2010

Self-similar random fields and rescaled random balls models

Hermine Biermé
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Anne Estrade
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Ingemar Kaj
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Résumé

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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Dates et versions

hal-00161614 , version 1 (11-07-2007)
hal-00161614 , version 2 (12-02-2008)

Identifiants

  • HAL Id : hal-00161614 , version 2

Citer

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