Bounds for clump size characteristics in the Boolean model

A random spatial coverage process whose generating point process is homogen eous Poisson, and whose attached random sets are independent and identicall y distributed, is called a Boolean model. Motivated by Blaszczyszyn et al. [1], distributional and higher moment properties of the size of clumps (con nected clusters of overlapping sets) in this model are derived. This provid es some complements to the result on the finiteness of the first moment pre sented in Hall [3]. The key idea is to construct a certain coupling process for a multitype branching process that dominates the clump size.