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Champs aléatoires: autosimilarité, anisotropie et étude directionnelle

Abstract : We study random fields that can modelize some porous media. We are mainly interested in second order statistics and focus on self-similarity properties. Under stationary assumptions, the field is characterized by a spectral measure. Asymptotic self-similarity properties are then given by the directional asymptotic homogeneity of the measure. Its parameter is given by the smallest coefficient of homogeneity in a logarithmic scale. To recover anisotropy one can perform a Radon transform of the field for which the self-similarity parameter depends on the direction. These second order results are well adapted to Gaussian models. In this case, the self-similarity parameter can be estimated with the quadratic variations. We consider injectivity problems for the Radon transform. In the last part, we study a Poissonian model obtained by small aggregated balls. Self-similarity properties are similar for second order statistics but unusual for convergence in law.
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Contributor : Hermine Biermé <>
Submitted on : Wednesday, September 21, 2005 - 1:28:37 AM
Last modification on : Thursday, March 5, 2020 - 6:49:21 PM
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  • HAL Id : tel-00010227, version 1


Hermine Biermé. Champs aléatoires: autosimilarité, anisotropie et étude directionnelle. Mathématiques [math]. Université d'Orléans, 2005. Français. ⟨tel-00010227⟩



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