Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22662
Barbour, A D; Greenwood, P (1993). Rates of Poisson approximation to finite range random fields. Annals of Applied Probability, 3(1):91-102.
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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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|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|
|Deposited On:||12 Apr 2010 12:17|
|Last Modified:||05 Apr 2016 13:28|
|Publisher:||Institute of Mathematical Statistics|
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