Rates of Poisson approximation to finite range random fields (Q1210484)

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.