On Stein's Factors for Poisson Approximation in Wasserstein Distance with Nonlinear Transportation Costs

Abstract

We establish various bounds on the solutions to a Stein equation for Poisson approximation in the Wasserstein distance with nonlinear transportation costs. The proofs are a refinement of those in Barbour and Xia (Bernoulli 12:943–954, 2006) using the results in Liu and Ma (Ann Inst H Poincaré Probab Stat 45:58–69, 2009). As a corollary, we obtain an estimate of Poisson approximation error measured in the L2-Wasserstein distance.