Macroscopic analysis of shot-noise Cox random balls

Adrien Clarenne (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we consider a cluster model of weighted Euclidean random balls generated by a shot-noise Cox process. It is an example of cluster point process. We perform a scaling on the model by shrinking the radii of the balls and compensate this effect by increasing the (mean) number of balls in each cluster, or/and increasing the (mean) number of clusters. We consider two different scenarios, say a local and a global scenarios. Heuristically, in the first scenario, we focus on the mean number of large balls in a cluster while in the second one, we focus on the global mean number of large balls in the model. According to the different scenarios, the cluster structure can persist at the limit or disappear.

Mots clés: random fields; limit theorem.; random balls; Cox processes

Domaines: Probabilités [math.PR]

Adrien Clarenne. Macroscopic analysis of shot-noise Cox random balls. Journal of Mathematical Analysis and Applications, 2019, 480 (1), pp.art. no. 123390. ⟨10.1016/j.jmaa.2019.123390⟩. ⟨hal-01946995⟩