Poisson random balls: self-similarity and X-ray images

Abstract : We study a random field obtained by counting the number of balls containing a given point, when overlapping balls are thrown at random according to a Poisson random measure. We describe a microscopic process which exhibits a multifractional behavior. We are particularly interested in the local asymptotical self-similarity (lass) properties of the field, as well as in its X-ray transforms. We obtain two different lass properties when considering the asymptotics either "in law" or "in the sense of second-order moments" and prove a relationship between the lass behavior of the field and the lass behavior of its X-ray transform. These results can be used to model and analyze porous media, images or connection networks.
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Article dans une revue
Advances in Applied Probability, Applied Probability Trust, 2006, 38, pp.853-872
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https://hal.archives-ouvertes.fr/hal-00170277
Contributeur : Anne Estrade <>
Soumis le : vendredi 7 septembre 2007 - 10:03:58
Dernière modification le : mardi 11 octobre 2016 - 14:11:11

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  • HAL Id : hal-00170277, version 1

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Hermine Biermé, Anne Estrade. Poisson random balls: self-similarity and X-ray images. Advances in Applied Probability, Applied Probability Trust, 2006, 38, pp.853-872. <hal-00170277>

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