Stein's method and Papangelou intensity for Poisson or Cox process approximation

Abstract

In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Poisson point process. We show that the so-called Kantorovich-Rubinstein distance between such a measure and another finite point process is bounded by the $L^1$-distance between their respective Papangelou intensities. Then, we deduce some convergence rates for sequences of point processes approaching a Poisson or a Cox point process.

Cited by in corpus (1)

• Multivariate Poisson and Poisson process approximations with applications to Bernoulli sums and $U$-statistics