On the rate of Poisson process approximation to a Bernoulli process

This note gives the rate for a Wasserstein distance between the distribution of a Bernoulli process on discrete time and that of a Poisson process, using Stein's method and Palm theory. The result here highlights the possibility that the logarithmic factor involved in the upper bounds established by Barbour and Brown and Barbour et al. may be superfluous in the true Wasserstein distance between the distributions of a point process and a Poisson process.