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Point processes in time and Stein's method


Barbour, A D; Brown, T; Xia, A (1998). Point processes in time and Stein's method. Stochastics and Stochastics Reports, 65(1-2):127-151.

Abstract

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.

Abstract

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.

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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
Uncontrolled Keywords:Immigration-death process; simple point process; compensator; predictable projection; optional projection; Wasserstein metric; Poisson approximation; coupling;
Language:English
Date:1998
Deposited On:07 Apr 2010 13:49
Last Modified:05 Apr 2016 13:26
Publisher:Taylor & Francis
ISSN:1026-7794
Additional Information:This is an electronic version of an article published in [Stochastics Stochastics Rep. 65 (1998), no. 1-2, 127--151]. Stochastics and Stochastics Reports is available online at: http://www.informaworld.com/smpp/title~db=all~content=t713652481
Publisher DOI:https://doi.org/10.1080/17442509808834176

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