Point processes in time and stein's method

• Published in: Stochastics and stochastics reports Vol. 65; no. 1-2; pp. 127 - 151
• Main Authors: Barbour, A. D., Brown, Timothy C., Xia, Aihua
• Format: Journal Article
• Language: English
• 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
• ISSN: 1045-1129
• DOI: 10.1080/17442509808834176

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...