Berry-Esseen for Free Random Variables
概率论
2007-09-03 v3 算子代数
摘要
An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n^{-1/2}, the same as in the classical case. An example with binomial measures shows that this estimate cannot be improved without imposing further restrictions on convolved measures.
引用
@article{arxiv.math/0610072,
title = {Berry-Esseen for Free Random Variables},
author = {Vladislav Kargin},
journal= {arXiv preprint arXiv:math/0610072},
year = {2007}
}
备注
15 pages, accepted to the Journal of Theoretical Probability, minor typos are corrected in versions 2 and 3