Point processes in time and stein's method

This article gives an upper bound for a Wasserstein distance between the distribution of a simple point process and that of a Poisson process on the positive half line. The bound is partly expressed in terms of their compensators, and partly in terms of the expected future effect of having a point a...

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Bibliographic Details
Published inStochastics and stochastics reports Vol. 65; no. 1-2; pp. 127 - 151
Main Authors Barbour, A. D., Brown, Timothy C., Xia, Aihua
Format Journal Article
LanguageEnglish
Published Gordon and Breach Science Publishers 01.12.1998
Subjects
compensator
coupling
Immigration-death process
Mathematics Subject Classification 1991: 60G55
optional projection
Poisson approximation
predictable projection
simple point process
Wasserstein metric
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Summary:This article gives an upper bound for a Wasserstein distance between the distribution of a simple point process and that of a Poisson process on the positive half line. The bound is partly expressed in terms of their compensators, and partly in terms of the expected future effect of having a point at a given time. The argument is based on Stein's method, together with a martingale approach. Some examples are provided, which illustrate the computation of the upper bound and demonstrate its accuracy
ISSN:1045-1129
DOI:10.1080/17442509808834176