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.
Publié le : 1975-12-14
Classification:
Approximation theorem,
convolutions,
probability measures,
$L_p$ approximation,
large deviation,
Poisson binomial distribution,
Poisson approximation,
60B10,
60B15,
60F05,
60F10
@article{1176996224,
author = {Chen, Louis H. Y.},
title = {An Approximation Theorem for Convolutions of Probability Measures},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 992-999},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996224}
}
Chen, Louis H. Y. An Approximation Theorem for Convolutions of Probability Measures. Ann. Probab., Tome 3 (1975) no. 6, pp. 992-999. http://gdmltest.u-ga.fr/item/1176996224/