Quick Search:

uzh logo
Browse by:

Zurich Open Repository and Archive

Barbour, A D; Brown, T (1992). Stein's method and point process approximation. Stochastic Processes and their Applications, 43(1):9-31.

Full text not available from this repository.

View at publisher


The Stein-Chen method for Poisson approximation is adapted into a form suitable for obtaining error estimates for the approximation of the whole distribution of a point process on a suitable topological space by that of a Poisson process. The adaptation involves consideration of an immigration-death process on the topological space, whose equilibrium distribution is that of the approximating Poisson process; the Stein equation has a simple interpretation in terms of the generator of the immigration-death process. The error estimates for process approximation in total variation do not have the ‘magic’ Stein-Chein multiplying constants, which for univariate approximation tend to zero as the mean gets larger, but examples, including Bernoulli trials and the hard-core model on the torus, show that this is not possible. By choosing weaker metrics on the space of distributions of point processes, it is possible to reintroduce these constants. The proofs actually yield an improved estimate for one of the constants in the univariate case.


45 citations in Web of Science®
44 citations in Scopus®
Google Scholar™


Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Deposited On:04 Nov 2009 14:37
Last Modified:05 Apr 2016 13:28
Free access at:Related URL. An embargo period may apply.
Publisher DOI:10.1016/0304-4149(92)90073-Y
Related URLs:http://user.math.uzh.ch/barbour/pub/Barbour/BBrown_PointProcess.pdf

Users (please log in): suggest update or correction for this item

Repository Staff Only: item control page