Estimates for the strong approximation in multidimensional central limit theorem

Details Estimates for the strong approximation in multidimensional central limit theorem Estimates for the strong approximation in multidimensional central limit theorem

2003-04-24

arxiv.org/abs/math/0304373v1

Proceedings of the ICM, Beijing 2002, vol. 3, 107--116

Mathematics

Probability

Scientific paper

In a recent paper the author obtained optimal bounds for the strong Gaussian approximation of sums of independent $\R^d$-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 $d$ and on distributions of summands is given explicitly. Some related problems are discussed.

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