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| HAL: hal-00161614, version 2 |
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| Journal of theoretical probabability 23, 4 (2010) 1110-1141 |
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| Available versions: | v1 (2007-07-11) | v2 (2008-02-12) |
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| Self-similar random fields and rescaled random balls models |
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| Hermine Biermé 1Anne Estrade 1 |
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| For the This work was supported by ANR grant ``mipomodim'' NT05-1-42030 collaboration(s) |
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| (2010) |
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| 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. |
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| 1: | Mathématiques appliquées Paris 5 (MAP5) |
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CNRS : UMR8145 – Université Paris V - Paris Descartes |
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| 2: | Department of Mathematics [Uppsala] |
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Uppsala Universitet |
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| Subject | : | Mathematics/Probability |
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| self-similarity – generalized random field – Poisson point process – fractional field – fractional Brownian motion |
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| Attached file list to this document: | ||||||||||
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| hal-00161614, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00161614 | |
| oai:hal.archives-ouvertes.fr:hal-00161614 | |
| From: Hermine Biermé | |
| Submitted on: Tuesday, 12 February 2008 17:05:39 | |
| Updated on: Monday, 22 November 2010 09:51:40 | |
