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Journal of theoretical probabability 23, 4 (2010) 1110-1141

Versions disponibles :

v1 (11-07-2007)

v2 (12-02-2008)

Self-similar random fields and rescaled random balls models

Hermine Biermé 1, Anne Estrade 1, Ingemar Kaj 2

This work was supported by ANR grant ``mipomodim'' NT05-1-42030 Collaboration(s)

(2010)

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.

1 :	Mathématiques appliquées Paris 5 (MAP5)
	CNRS : UMR8145 – Université Paris V - Paris Descartes
2 :	Department of Mathematics [Uppsala]
	Uppsala Universitet

Équipe de recherche : MAP5 University of Paris Descartes, Department of mathematics Uppsala University

Domaine

:

Mathématiques/Probabilités

Mots Clés : self-similarity – generalized random field – Poisson point process – fractional field – fractional Brownian motion

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Contributeur : Hermine Biermé <>

Soumis le : Mardi 12 Février 2008, 17:05:39

Dernière modification le : Lundi 22 Novembre 2010, 09:51:40