Bounds for clump size characteristics in the Boolean model.

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