On metrics in point process approximation

Abstract

This paper improves some results of Barbour and Brown (1992) on approximation of a point process by a Poisson process. The approximations bound a Wasserstein distance, and here this distance is altered so as to permit the point process and the Poisson process to have different total mass. One approximation in Barbour and Brown (1992) hounds the Wasserstein distance by an average distance between the process and its reduced Palm process. Here the distance used in the bound is reduced so as to permit different total numbers of points and different locations for the points of the process and the reduced Palm process. Explicit relations between the Wasserstein and the Prohorov metrics are also considered