Estimates for the Strong Approximation in Multidimensional Central Limit Theorem

摘要

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 Komlos-major-Tusnady and Sakhanenko. The dependence of constants on the dimension d and on distributions of summands is given explicitly. Some related problems are discussed.