Stein's method, palm theory and poisson process approximation
成果类型：
Article
署名作者：
Chen, LHY; Xia, AH
署名单位：
National University of Singapore; University of Melbourne
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117904000000027
发表日期：
2004
页码：
2545-2569
关键词：
摘要：
The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem 2.3) in Poisson process approximation is proved by taking the local approach. It is obtained without reference to any particular metric, thereby allowing wider applicability. A Wasserstein pseudometric is introduced for measuring the accuracy of point process approximation. The pseudometric provides a generalization of many metrics used so far, including the total variation distance for random variables and the Wasserstein metric for processes as in Barbour and Brown [Stochastic Process. Appl. 43 (1992) 9-31]. Also, through the pseudometric, approximation for certain point processes on a given carrier space is carried out by lifting it to one on a larger space, extending an idea of Arratia, Goldstein and Gordon [Statist. Sci. 5 (1990) 403-434]. The error bound in the general result is similar in form to that for Poisson approximation. As it yields the Stein factor 1/lambda. as in Poisson approximation, it provides good approximation, particularly in cases where; is large. The general result is applied to a number of problems including Poisson process modeling of rare words in a DNA sequence.