Infinite dimensional functional convergences in random balls model

Jean-Christophe Breton (1) , Renan Gobard (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We consider a weighted random ball model generated by a Poisson measure. The macroscopic behaviour of the weight amassed on this model by a configuration has recently received attention. In this paper, we complement the previous finite dimensional distribution fluctuation results and propose functional convergences of such functionals on the set of configurations.

Mots clés: self-similarity; generalized random fields; functional convergence; tightness; Poisson point process

Domaines: Probabilités [math.PR]

Jean-Christophe Breton, Renan Gobard. Infinite dimensional functional convergences in random balls model. ESAIM: Probability and Statistics, 2015, 19, pp.782-793. ⟨10.1051/ps/2015016⟩. ⟨hal-01258513⟩