Geodesic
The accuracy of strong Gaussian approximation for sums of independent random vectors
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 4, pp. 721-761

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This paper is a survey of recent results on the accuracy of strong Gaussian approximation for sums of independent random vectors. They give multidimensional generalizations of one-dimensional results due to Komlós, Major, and Tusnády, as well as to Sakhanenko, and improve upon Einmahl's multidimensional results. Infinite-dimensional analogues of these results are also presented. Bibliography: 102 titles.
Keywords: multidimensional invariance principle, strong approximation, sums of independent random vectors. 
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     author = {A. Yu. Zaitsev},
     title = {The accuracy of strong {Gaussian} approximation for sums of independent random vectors},
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A. Yu. Zaitsev. The accuracy of strong Gaussian approximation for sums of independent random vectors. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 4, pp. 721-761. http://geodesic.mathdoc.fr/item/RM_2013_68_4_a2/