A Compact Law of the Iterated Logarithm for Random Vectors in the Generalized Domain of Attraction of the Multivariate Gaussian Law

Steven J. Sepanski ()
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Steven J. Sepanski: Saginaw Valley State University

Journal of Theoretical Probability, 1999, vol. 12, issue 3, 757-778

Abstract: Abstract For a sequence of independent identically distributed random vectors, we prove that the limiting cluster set of the appropriately operator normed partial sums is, with probability one, the closed unit euclidean ball. The result is proved under the hypotheses that the law of the random vectors belongs to the Generalized Domain of Attraction of the multivariate Gaussian law and satisfy a mild integrability condition. The two conditions together are still weaker than finite second normed moment and are necessary and sufficient.

Keywords: Law of the iterated logarithm; central limit theorem; generalized domain of attraction; operator normalization (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021632016642

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