Rates of Poisson approximation to finite range random fields
type: Item
instance of: scholarly article
title: Rates of Poisson approximation to finite range random fields
zbMATH Open document ID: 0784.60053
published in: The Annals of Applied Probability
publication date: 1994-04-06T00:00:00Z
review text: The Stein-Chen approach [see \textit{L. H. Y. Chen}, Ann. Probab. 3, 534-545 (1975; Zbl 0335.60016)] is used to obtain bounds on the Poisson approximation of a random field, in both a random variable and a stochastic process sense. The hypotheses are Dobrushin's condition or, alternatively, positive dependence combined with a bound on decay of correlations. Rates of convergence are derived.
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 179287
zbMATH Keywords: rates of convergence
zbMATH Keywords: Stein-Chen approach
zbMATH Keywords: Poisson approximation
zbMATH Keywords: Dobrushin's condition
author: A. D. Barbour
author: Priscilla Greenwood
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177005509
OpenAlex ID: W1965195457
DOI: 10.1214/AOAP/1177005509
Recommended article: Poisson Limit for Associated Random Fields
Recommended article: A note on the rate of Poisson approximation of empirical processes
Recommended article: Poisson and extreme value limit theorems for Markov random fields
Recommended article: On the rate of Poisson convergence
Recommended article: On the rate of Poisson approximation to Bernoulli partial sum processes
Recommended article: A rate of convergence in the Poissonian representation of stable distributions
Recommended article: Q5460980
description: scientific article; zbMATH DE number 179287