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April, 1986 A Semigroup Approach to Poisson Approximation
P. Deheuvels, D. Pfeifer
Ann. Probab. 14(2): 663-676 (April, 1986). DOI: 10.1214/aop/1176992536

Abstract

The aim of this paper is twofold: first, to show that Poisson approximation problems for independent summands can in a natural way be treated in a suitable operator semigroup framework, allowing at the same time for an asymptotically precise evaluation of the leading term with respect to the total variation distance; second, to determine asymptotically those Poisson distributions which minimize this distance for given Bernoulli summands. Besides semigroup methods, coupling techniques as well as direct computations are used.

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P. Deheuvels. D. Pfeifer. "A Semigroup Approach to Poisson Approximation." Ann. Probab. 14 (2) 663 - 676, April, 1986. https://doi.org/10.1214/aop/1176992536

Information

Published: April, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0597.60019
MathSciNet: MR832029
Digital Object Identifier: 10.1214/aop/1176992536

Subjects:
Primary: 60F05
Secondary: 20M30 , 47D05 , 62E20

Keywords: coupling techniques , operator semigroups , Poisson approximation

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 2 • April, 1986
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