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The law of the iterated logarithm for independent random variables with multidimensional parameters and its application. (English) Zbl 1050.60032

Summary: For a set of i.i.d. r.v. indexed by positive integer \(d\)-dimensional lattice points, and for some general normalizing sequence, we determine necessary and sufficient conditions for the law of iterated logarithm. As its application, we give conditions for the existence of moments of the supremum of normed partial sums.

MSC:

60F15 Strong limit theorems
60F05 Central limit and other weak theorems
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