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On the strong Gaussian approximation in multidimensional case. (English) Zbl 1055.60032

Summary: A multidimensional version of a result of J. Komlós, P. Major and G. Tusnády [Z. Wahrscheinlichkeitstheorie Verw. Geb. 32, 111–131 (1975; Zbl 0308.60029) and ibid. 34, 33–58 (1976; Zbl 0307.60045)] for sums of independent random vectors with finite exponential moments is proved.

MSC:

60F17 Functional limit theorems; invariance principles
60F15 Strong limit theorems
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