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December, 1975 An Approximation Theorem for Convolutions of Probability Measures
Louis H. Y. Chen
Ann. Probab. 3(6): 992-999 (December, 1975). DOI: 10.1214/aop/1176996224


An extension of the usual problem of bounding the total variation of the difference of two probability measures is considered for certain convolutions of probability measures on a measurable Abelian group. The result is a fairly general approximation theorem which also yields an $L_p$ approximation theorem and a large deviation result in some special cases. A limit theorem in equally general setting is proved as a consequence of the main theorem. As the convolutions of probability measures under consideration reduce to the Poisson binomial distribution as a special case, an alternative proof of the approximation theorem in this special case is discussed.


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Louis H. Y. Chen. "An Approximation Theorem for Convolutions of Probability Measures." Ann. Probab. 3 (6) 992 - 999, December, 1975.


Published: December, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0358.60010
MathSciNet: MR383483
Digital Object Identifier: 10.1214/aop/1176996224

Primary: 60B10
Secondary: 60B15 , 60F05 , 60F10

Keywords: $L_p$ approximation , Approximation theorem , Convolutions , large deviation , Poisson approximation , Poisson binomial distribution , probability measures

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 6 • December, 1975
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