• Bernoulli
  • Volume 15, Number 2 (2009), 550-568.

Stein’s method and Poisson process approximation for a class of Wasserstein metrics

Dominic Schuhmacher

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Based on Stein’s method, we derive upper bounds for Poisson process approximation in the L1-Wasserstein metric d2(p), which is based on a slightly adapted Lp-Wasserstein metric between point measures. For the case p=1, this construction yields the metric d2 introduced in [Barbour and Brown Stochastic Process. Appl. 43 (1992) 9–31], for which Poisson process approximation is well studied in the literature. We demonstrate the usefulness of the extension to general p by showing that d2(p)-bounds control differences between expectations of certain pth order average statistics of point processes. To illustrate the bounds obtained for Poisson process approximation, we consider the structure of 2-runs and the hard core model as concrete examples.

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Bernoulli, Volume 15, Number 2 (2009), 550-568.

First available in Project Euclid: 4 May 2009

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Barbour-Brown metric distributional approximation L_p-Wasserstein metric Poisson point process Stein’s method


Schuhmacher, Dominic. Stein’s method and Poisson process approximation for a class of Wasserstein metrics. Bernoulli 15 (2009), no. 2, 550--568. doi:10.3150/08-BEJ161.

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