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Rates of Poisson approximation to finite range random fields


Barbour, A D; Greenwood, P (1993). Rates of Poisson approximation to finite range random fields. Annals of Applied Probability, 3(1):91-102.

Abstract

The Stein-Chen approach 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 which supplement the limit theorems of Berman. The results have application to certain Gibbs states at both high and low temperature.

Abstract

The Stein-Chen approach 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 which supplement the limit theorems of Berman. The results have application to certain Gibbs states at both high and low temperature.

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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:Poisson approximation; Stein-Chen method; random fields; Gibbs states; extrema
Language:English
Date:1993
Deposited On:12 Apr 2010 12:17
Last Modified:05 Apr 2016 13:28
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
Publisher DOI:https://doi.org/10.1214/aoap/1177005509

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