Geodesic
On the estimates of the rate of convergence in the invariance principle for Banach spaces
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 734-744

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We propose a method for obtaining the estimates in the invariance principle for Banach spaces; this method doesn't use the representation on a common probability space. In particular, it is shown that the estimate proved by Borovkov [7] for the one- dimensional invariance principle remains valid for the finite-dimensional case too. 
@article{TVP_1980_25_4_a4,
     author = {A. A. Borovkov and A. I. Sahanenko},
     title = {On the estimates of the rate of convergence in the invariance principle for {Banach} spaces},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {734--744},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a4/}
}
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A. A. Borovkov; A. I. Sahanenko. On the estimates of the rate of convergence in the invariance principle for Banach spaces. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 734-744. http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a4/