UZH-Logo

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.

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.

Altmetrics

Downloads

41 downloads since deposited on 07 Apr 2010
10 downloads since 12 months
Detailed statistics

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:10.1080/17442509808834176
Permanent URL: http://doi.org/10.5167/uzh-22170

Download

[img]
Preview
Filetype: PDF (Preprint)
Size: 1MB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations