Distance estimates for dependent thinnings of point processes with densities

Details Distance estimates for dependent thinnings of point processes with densities Distance estimates for dependent thinnings of point processes with densities

2007-01-25

arxiv.org/abs/math/0701728v1

Mathematics

Probability

31 pages; submitted

Scientific paper

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 such processes we can apply a corresponding result directly without the detour of discretization and thus obtain better and more natural bounds not only in d_2 but also in the stronger total variation metric. We give applications for thinning by covering with an independent Boolean model and "Mat{\'e}rn 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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