Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 15, Number 1B (2005), 615-651.
Upper bounds for spatial point process approximations
We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646–659] that, under mild assumptions, the transformed processes behave approximately like Poisson processes for large T. In this article, under very similar assumptions, explicit upper bounds are given for the d2-distance between the corresponding point process distributions. A number of related results, and applications to kernel density estimation and long range dependence testing are also presented. The main results are proved by applying a generalized Stein–Chen method to discretized versions of the point processes.
Ann. Appl. Probab., Volume 15, Number 1B (2005), 615-651.
First available in Project Euclid: 1 February 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Schuhmacher, Dominic. Upper bounds for spatial point process approximations. Ann. Appl. Probab. 15 (2005), no. 1B, 615--651. doi:10.1214/105051604000000684. https://projecteuclid.org/euclid.aoap/1107271662