Open Access
February, 1993 Rates of Poisson Approximation to Finite Range Random Fields
A. D. Barbour, P. E. Greenwood
Ann. Appl. Probab. 3(1): 91-102 (February, 1993). DOI: 10.1214/aoap/1177005509


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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A. D. Barbour. P. E. Greenwood. "Rates of Poisson Approximation to Finite Range Random Fields." Ann. Appl. Probab. 3 (1) 91 - 102, February, 1993.


Published: February, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0784.60053
MathSciNet: MR1202517
Digital Object Identifier: 10.1214/aoap/1177005509

Primary: 60G60
Secondary: 60G55

Keywords: Extrema , Gibbs states , Poisson approximation , Random fields , Stein-Chen method

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.3 • No. 1 • February, 1993
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