2010/02/26 by Jean-Christophe Breton, Breton, Jean-Christophe, Clément Dombry +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #60F17 (primary) #60G18 #60G60 #60H05 (secondary) #Bayesian Methods and Mixture Models #FOS: Mathematics #Geometry and complex manifolds #Point processes and geometric inequalities #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1002.4985
openalex publication_date 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a generalization of the weighted random ball model. The model is\ndriven by a random Poisson measure with a product heavy tailed intensity\nmeasure. Such a model typically represents the transmission of a network of\nstations with a fading effect. In a previous article, the authors proved the\nconvergence of the finite-dimensional distributions of related generalized\nrandom fields under various scalings and in the particular case when the fading\nfunction is the indicator function of the unit ball. In this paper, tightness\nand functional convergence are investigated. Using suitable moment estimates,\nwe prove functional convergences for some parametric classes of configurations\nunder the so-called large ball scaling and intermediate ball scaling.\nConvergence in the space of distributions is also discussed.\n