On Stein's factors for Poisson approximation in Wasserstein distance with non-linear transportation costs

TL;DR

This paper develops bounds on solutions to Stein equations for Poisson approximation under non-linear Wasserstein distances, refining previous methods and providing error estimates in L^2-Wasserstein distance.

Contribution

It introduces new bounds for Stein equations in Wasserstein distance with non-linear costs, improving upon prior approaches and extending error estimation techniques.

Findings

Derived bounds for Stein solutions in non-linear Wasserstein distances

Refined existing proofs using Liu and Ma's results

Provided L^2-Wasserstein distance error estimates

Abstract

We establish various bounds on the solutions to a Stein equation for Poisson approximation in Wasserstein distance with non-linear transportation costs. The proofs are a refinement of those in [Barbour and Xia (2006)] using the results in [Liu and Ma (2009)]. As a corollary, we obtain an estimate of Poisson approximation error measured in L^2-Wasserstein distance.