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

Zhong-Wei Liao (), Yutao Ma () and Aihua Xia ()
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Zhong-Wei Liao: Beijing Normal University at Zhuhai
Yutao Ma: Beijing Normal University
Aihua Xia: The University of Melbourne

Journal of Theoretical Probability, 2022, vol. 35, issue 4, 2383-2412

Abstract: 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 $$L^2$$ L 2 -Wasserstein distance.

Keywords: Poisson approximation; Wasserstein distance; Stein’s factors; Primary 60F05; Secondary 60E15; 60J27 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01129-x

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