Summary
An estimate of the convergence speed in the multidimensional invariance principle is obtained. Using this estimate, we can prove strong invariance principles for partial sums of independent not necessarily identically distributed multidimensional random vectors.
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Einmahl, U. A useful estimate in the multidimensional invariance principle. Probab. Th. Rel. Fields 76, 81–101 (1987). https://doi.org/10.1007/BF00390277
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DOI: https://doi.org/10.1007/BF00390277