Refined convergence for the Boolean model

Abstract : In a previous work, two of the authors proposed a new proof of a well known convergence result for the scaled elementary connected vacant component in the high intensity Boolean model towards the Crofton cell of the Poisson hyperplane process. In this paper, we consider the particular case of the two-dimensional Boolean model where the grains are discs with random radii. We investigate the second-order term in this convergence when the Boolean model and the Poisson line process are coupled on the same probability space. A precise coupling between the Boolean model and the Poisson line process is first established, a result of directional convergence in distribution for the difference of the two sets involved is derived as well.
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Article dans une revue
Advances in Applied Probability, Applied Probability Trust, 2009, 41 (4), pp.940-957
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https://hal.archives-ouvertes.fr/hal-00274553
Contributeur : Pierre Calka <>
Soumis le : vendredi 29 mai 2009 - 15:53:21
Dernière modification le : jeudi 9 février 2017 - 16:05:19
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 12:57:41

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  • HAL Id : hal-00274553, version 2
  • ARXIV : 0804.3088

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Pierre Calka, Julien Michel, Katy Paroux. Refined convergence for the Boolean model. Advances in Applied Probability, Applied Probability Trust, 2009, 41 (4), pp.940-957. <hal-00274553v2>

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