Stein's method and poisson process convergence
Author:
- A. D. BarbourABA. D. Barbour
- 1 January 1988
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (A) , 175-184
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.Keywords
This publication has 9 references indexed in Scilit:
- An Improved Error Bound for the Compound Poisson Approximation of a Nearly Homogeneous PortfolioASTIN Bulletin, 1987
- On the rate of Poisson convergenceMathematical Proceedings of the Cambridge Philosophical Society, 1984
- On the rates in the central limit theorem for weakly dependent random fieldsProbability Theory and Related Fields, 1983
- Poisson convergence and random graphsMathematical Proceedings of the Cambridge Philosophical Society, 1982
- Equilibrium distributions Markov population processesAdvances in Applied Probability, 1980
- Two central limit problems for dependent random variablesProbability Theory and Related Fields, 1978
- Poisson Approximation for Dependent TrialsThe Annals of Probability, 1975
- Uniform rates of convergence for Markov chain transition probabilitiesProbability Theory and Related Fields, 1974
- A Bound for the Error in the Normal Approximation to the Distribution of a Sum of Dependent Random Variables1972