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Zbl 0675.60017
Arratia, R.; Goldstein, L.; Gordon, L.
Two moments suffice for Poisson approximations: The Chen-Stein method. (English)
[J] Ann. Probab. 17, No.1, 9-25 (1989). ISSN 0091-1798

In {\it L. H. Y. Chen} [Ann. Probab. 3, 534-545 (1975; Zbl 0335.60016)], Stein's method of obtaining rates of convergence near a normal limit was adapted for use in the Poisson context. The Stein-Chen method which resulted has turned out to be one of the most powerful methods available for establishing Poisson approximations for sums of dependent indicator random variables. \par In the present paper, the authors illustrate this with a variety of instructive examples, mainly in the context of random sequences and matchings. They also prove an important process generalization of Chen's theorem; an alternative approach to process approximation was given by the reviewer [J. Appl. Probab., Spec. Vol. 25A, 175-184 (1988; Zbl 0661.60034)].
[A.D.Barbour]

MSC 2000:: *60F05 Weak limit theorems
60F17 Functional limit theorems
60C05 Combinatorial probability

Keywords: Stein's method; Poisson approximations; matchings

Citations: Zbl 0335.60016; Zbl 0661.60034

Cited in: Zbl 0888.62015

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