Fractional Poisson Fields

Abstract : This paper considers random balls in a D-dimensional Euclidean space whose centers are prescribed by a homogeneous Poisson point process and whose radii are prescribed by a specific power law. A random field is constructed by counting the number of covering balls at each point. Even though it is not Gaussian, this field shares the same covariance function as the fractional Brownian field (fBf). By analogy it is called fractional Poisson field (fPf). In this paper, we are mainly interested in the simulation of fPfs with index H in (0,1/2) and in the estimation of the H index. Our method is based on the analysis of structure functions. The fPf exhibits a multifractal behavior, contrary to that of the fBf which is monofractal.
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Pré-publication, Document de travail
MAP5 2009-13. 2009
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Contributeur : Hermine Biermé <>
Soumis le : vendredi 8 mai 2009 - 20:11:38
Dernière modification le : mardi 10 octobre 2017 - 11:22:04
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  • HAL Id : hal-00382570, version 1

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Hermine Biermé, Yann Demichel, Anne Estrade. Fractional Poisson Fields. MAP5 2009-13. 2009. 〈hal-00382570〉

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