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2009 Distance estimates for dependent thinnings of point processes with densities
Dominic Schuhmacher
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Electron. J. Probab. 14: 1080-1116 (2009). DOI: 10.1214/EJP.v14-643


In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance $d_2$ between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization with a result based on Stein's method. In the present article we concentrate on point processes that have a density with respect to a Poisson process, for which we can apply a corresponding result directly without the detour of discretization. This enables us to obtain better and more natural bounds in the $d_2$-metric, and for the first time also bounds in the stronger total variation metric. We give applications for thinning by covering with an independent Boolean model and "Matern type I" thinning of fairly general point processes. These applications give new insight into the respective models, and either generalize or improve earlier results.


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Dominic Schuhmacher. "Distance estimates for dependent thinnings of point processes with densities." Electron. J. Probab. 14 1080 - 1116, 2009.


Accepted: 26 May 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1196.60089
MathSciNet: MR2506126
Digital Object Identifier: 10.1214/EJP.v14-643

Primary: 60G55
Secondary: 60D05 , 60E99

Keywords: Barbour-Brown distance , point process , point process density , Poisson process approximation , Random field , Stein's method , thinning , total variation distance

Vol.14 • 2009
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