Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments

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.