# Stein's method and Papangelou intensity for Poisson or Cox process approximation

Abstract : In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Pois-son point process. We show that the so-called Kantorovich-Rubinstein distance between such a measure and another finite point process is bounded by the $L^1$-distance between their respective Papangelou intensities. Then, we deduce some convergence rates for sequences of point processes approaching a Poisson or a Cox point process.
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Cited literature [47 references]

https://hal.archives-ouvertes.fr/hal-01832212
Contributor : Laurent Decreusefond <>
Submitted on : Friday, July 6, 2018 - 5:31:18 PM
Last modification on : Tuesday, December 8, 2020 - 10:21:50 AM
Long-term archiving on: : Tuesday, October 2, 2018 - 5:36:47 AM

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• HAL Id : hal-01832212, version 1

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Laurent Decreusefond, Aurélien Vasseur. Stein's method and Papangelou intensity for Poisson or Cox process approximation. 2018. ⟨hal-01832212⟩

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