Spatial Poisson point processes are typically used to model the random scattering of configuration points within a plane or a three-dimensional space \({\mathord {\mathbb X}}\). In case \({\mathord {\mathbb X}}= {\mathord {\mathbb R}}_+\) is the real half line, these random points can be identified with the jump times \((T_k)_{k \ge 1}\) of the standard Poisson process \((N_t)_{t\in {\mathord {\mathbb R}}_+}\) introduced in Sect. 9.1. However, in contrast with the previous chapter, no time ordering is a priori imposed here on the index set \({\mathord {\mathbb X}}\).