Bernoulli

  • 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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 4 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.bj/1241444902

Digital Object Identifier
doi:10.3150/08-BEJ161

Mathematical Reviews number (MathSciNet)
MR2543874

Zentralblatt MATH identifier
1204.60039

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

Citation

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. https://projecteuclid.org/euclid.bj/1241444902


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