Geodesic
On the rate of convergence for the multidimensiona invariance principle
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 642-649

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In this paper, estimates of [1], [2] are generalized under some additional restrictions for the convergence to 1) a multidimensional Wiener process, 2) a Brownian sheet, i.e. a Gaussian random field $w(t)$, $t\in[0,1]$, $q>1$: $$ \mathbf Ew(t)=0,\quad\mathbf Ew(t)w(s)=\prod_1^q(t_i\wedge s_i). $$ 
@article{TVP_1975_20_3_a14,
     author = {V. V. Gorodestkii},
     title = {On the rate of convergence for the multidimensiona invariance principle},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {642--649},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a14/}
}
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V. V. Gorodestkii. On the rate of convergence for the multidimensiona invariance principle. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 642-649. http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a14/