Header

UZH-Logo

Maintenance Infos

Distance estimates for dependent superpositions of point processes


Schuhmacher, D (2005). Distance estimates for dependent superpositions of point processes. Stochastic Processes and their Applications, 115(11):1819-1837.

Abstract

In this article, superpositions of possibly dependent point processes on a general space View the MathML source are considered. Using Stein's method for Poisson process approximation, an estimate is given for the Wasserstein distance d2 between the distribution of such a superposition and an appropriate Poisson process distribution. This estimate is compared to a modern version of Grigelionis’ theorem, and to results of Banys [Lecture Notes in Statistics, vol. 2, Springer, New York, 1980, pp. 26–37], Arratia et al. [Ann. Probab. 17 (1989) 9–25] and Barbour et al. [Poisson Approximation, Oxford University Press, Oxford, 1992]. Furthermore, an application to a spatial birth–death model is presented.

Abstract

In this article, superpositions of possibly dependent point processes on a general space View the MathML source are considered. Using Stein's method for Poisson process approximation, an estimate is given for the Wasserstein distance d2 between the distribution of such a superposition and an appropriate Poisson process distribution. This estimate is compared to a modern version of Grigelionis’ theorem, and to results of Banys [Lecture Notes in Statistics, vol. 2, Springer, New York, 1980, pp. 26–37], Arratia et al. [Ann. Probab. 17 (1989) 9–25] and Barbour et al. [Poisson Approximation, Oxford University Press, Oxford, 1992]. Furthermore, an application to a spatial birth–death model is presented.

Statistics

Citations

4 citations in Web of Science®
4 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

15 downloads since deposited on 04 Nov 2009
0 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2005
Deposited On:04 Nov 2009 15:01
Last Modified:06 Dec 2017 20:47
Publisher:Elsevier
ISSN:0304-4149
Publisher DOI:https://doi.org/10.1016/j.spa.2005.06.004
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2172888
http://arxiv.org/abs/math/0701728

Download

Download PDF  'Distance estimates for dependent superpositions of point processes'.
Preview
Content: Accepted Version
Filetype: PDF
Size: 438kB