Piling of multiscale random models

This paper considers random balls in a D-dimensional Euclidean space whose centers are prescribed by a homogeneous Poisson point process and whose radii are forced to be in a finite interval with a power-law distribution. Random fields are constructed by counting the number of covering balls at each point. We are mainly interested in the simulation of these fields and in the empirical estimation of its index H. Finally simulations are given.