## Annals of Probability

### An Approximation Theorem for Convolutions of Probability Measures

Louis H. Y. Chen

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 3, Number 6 (1975), 992-999.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996224

Digital Object Identifier
doi:10.1214/aop/1176996224

Mathematical Reviews number (MathSciNet)
MR383483

Zentralblatt MATH identifier
0358.60010

JSTOR