We consider a Poisson process Phi on a general phase space. The expectation of a function of Phi can be considered as a functional of the intensity measure lambda of Phi. Extending ealier results of Molchanov and Zuyev (2000) on finite Poisson processes, we will study the behaviour of this functional under signed (possibly infinite) perturbations of lambda. A key ingredient of our approach is the explicit Fock space representation obtained in Last and Penrose (2011). As an application we will discuss the infinite cluster in a supercitical Boolean model.
This part of the talk is based on joint work with Sergei Zuyev.