03 - Self-similar random fields and rescaled random balls models - Hermine BIERME

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 limiting generalized random fields viewed as continuous random linear functionals. Joint work with A. Estrade (Paris 5) and Ingemar Kaj (Uppsala University) Hermine BIERME Université René Descartes Paris 5 Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1207750733740 (pdf) Ecouter l'intervention : Bande son disponible au format mp3 Durée : 41 mn