Poisson approximation, compensators and coupling

Abstract

We use coupling method to estimate a Wasserstein distance between a simple point process and a Poisson process in terms of their compensators. The Wasserstein distance of two probability measures Q1 and Q2 on configuration space of point processes on [0, T] is defined as the sum of two parts: under a best coupling (X1, X2) of Q1 and Q2, the first part is P(|X1| ≠ |X2|) and the second part is comparison between the locations of X1 and X2 on [|X1| = |X2|]. Although the coupling method is not very successful in estimating the first part, we prove in this paper that this method can be applied to establish accurate upper bound for the second part. In some cases, the coupling argument can produce ..