Dependence orderings for some functionals of multivariate point processes

We study dependence orderings for functionals of k-variate point processes [Phi] and [Psi]. We view the first process as a collection of counting measures, whereas the second as the sequences of interpoint distances. Subsequently, we establish regularity properties of stationary sequences which generalize known results for iid case. The theoretical results are illustrated by many special cases including comparison of multivariate sums and products, comparison of multivariate shock models and queueing systems.