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Distance estimates for Poisson process approximations of dependent thinnings


Schuhmacher, D (2005). Distance estimates for Poisson process approximations of dependent thinnings. Electronic Journal of Probability, 10(5):165-201.

Abstract

It is well known, that under certain conditions, gradual thinning of a point process on R+d, accompanied by a contraction of space to compensate for the thinning, leads in the weak limit to a Cox process. In this article, we apply discretization and a result based on Stein's method to give estimates of the Barbour-Brown distance d2 between the distribution of a thinned point process and an approximating Poisson process, and evaluate the estimates in concrete examples. We work in terms of two, somewhat different, thinning models. The main model is based on the usual thinning notion of deleting points independently according to probabilities supplied by a random field. In Section 4, however, we use an alternative thinning model, which can be more straightforward to apply if the thinning is determined by point interactions. ~

Abstract

It is well known, that under certain conditions, gradual thinning of a point process on R+d, accompanied by a contraction of space to compensate for the thinning, leads in the weak limit to a Cox process. In this article, we apply discretization and a result based on Stein's method to give estimates of the Barbour-Brown distance d2 between the distribution of a thinned point process and an approximating Poisson process, and evaluate the estimates in concrete examples. We work in terms of two, somewhat different, thinning models. The main model is based on the usual thinning notion of deleting points independently according to probabilities supplied by a random field. In Section 4, however, we use an alternative thinning model, which can be more straightforward to apply if the thinning is determined by point interactions. ~

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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:25 February 2005
Deposited On:16 Nov 2009 20:42
Last Modified:21 Nov 2017 14:21
Publisher:Institute of Mathematical Statistics
ISSN:1083-6489
Official URL:http://www.emis.de/journals/EJP-ECP/_ejpecp/viewarticle4d5f.html?id=1492
Related URLs:http://www.math.washington.edu/~ejpecp/

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