Two moments suffice for Poisson approximations: The Chen-Stein method. (English) Zbl 0675.60017

In 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.
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)].
Reviewer: A.D.Barbour


60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
60C05 Combinatorial probability
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