Annals of Probability
- Ann. Probab.
- Volume 3, Number 6 (1975), 992-999.
An Approximation Theorem for Convolutions of Probability Measures
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.
Ann. Probab., Volume 3, Number 6 (1975), 992-999.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60B10: Convergence of probability measures
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 60F05: Central limit and other weak theorems 60F10: Large deviations
Chen, Louis H. Y. An Approximation Theorem for Convolutions of Probability Measures. Ann. Probab. 3 (1975), no. 6, 992--999. doi:10.1214/aop/1176996224. https://projecteuclid.org/euclid.aop/1176996224