Geodesic
Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 110-121

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The aim of this paper is to derive consequences of a result of Götze and Zaitsev (2008). It is shown that in the case of i.i.d. summands this result implies a multidimensional version of some results of Sakhanenko (1985) We establish bounds for the rate of strong Gaussian approximation of sums of independent $\mathbf R^d$-valued random vectors $\xi_j$ having finite moments $\mathbf E\|\xi_j\|^\gamma$, $\gamma\ge2$. Bibl. – 13 titles. 
@article{ZNSL_2009_368_a7,
     author = {F. G\"otze and A. Yu. Zaitsev},
     title = {Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {110--121},
     publisher = {mathdoc},
     volume = {368},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a7/}
}
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F. Götze; A. Yu. Zaitsev. Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 110-121. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a7/