Estimates for the strong approximation in multidimensional central limit theorem
Probability
2007-05-23 v1
Abstract
In a recent paper the author obtained optimal bounds for the strong Gaussian approximation of sums of independent -valued random vectors with finite exponential moments. The results may be considered as generalizations of well-known results of Koml\'os--Major--Tusn\'ady and Sakhanenko. The dependence of constants on the dimension and on distributions of summands is given explicitly. Some related problems are discussed.
Cite
@article{arxiv.math/0304373,
title = {Estimates for the strong approximation in multidimensional central limit theorem},
author = {A. Yu. Zaitsev},
journal= {arXiv preprint arXiv:math/0304373},
year = {2007}
}