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Short Communications

On the Law of the Iterated Logarithm for Operator Normed Sums of Random Vectors

V. A. Koval'

National Technical University of Ukraine "Kiev Polytechnic Institute"

Abstract: This paper proves the law of the iterated logarithm for sums of random vectors in $\mathbf{R}^k$ normed by linear operators of general type. We suppose that the sequence of the random vectors satisfies Strassen's invariance principle.

Keywords: law of the iterated logarithm, almost sure invariance principle, operator normed sums of random vectors.

Received: 09.08.1999

DOI: 10.4213/tvp3927

 English version: Theory of Probability and its Applications, 2002, 46:2, 366–368

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