On the rate of Poisson process approximation to a Bernoulli process

Abstract

The main result of the paper is a refinement of Xia's (1997) bound on the Kantorovich distance between distributions of a Bernoulli point process and an approximating Poisson process. In particular, we show that the distance between distributions of a Bernoulli point process and the Poisson process with the same mean measure has the order of the total variation distance between the laws of the total masses of these processes.