Stein's method and poisson process convergence

Author:

Barbour A. D.

Abstract

Stein's method of obtaining rates of convergence, well known in normal and Poisson approximation, is considered here in the context of approximation by Poisson point processes, rather than their one-dimensional distributions. A general technique is sketched, whereby the basic ingredients necessary for the application of Stein's method may be derived, and this is applied to a simple problem in Poisson point process approximation.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference11 articles.

1. On the rates in the central limit theorem for weakly dependent random fields

2. A bound for the error in the normal approximation to the distribution of a sum of dependent random variables;Stein;Proc. 6th Berkeley Symp. Math. Statist. Prob.,1970

3. Karr A. F. and Serfling R. J. (1987) Poisson approximation of Bernoulli point processes and their superpositions, via coupling.

4. Two central limit problems for dependent random variables

5. Poisson convergence and random graphs

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