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

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  • Steven J. Sepanski

    (Saginaw Valley State University)

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.

Suggested Citation

  • Steven J. Sepanski, 1999. "A Compact Law of the Iterated Logarithm for Random Vectors in the Generalized Domain of Attraction of the Multivariate Gaussian Law," Journal of Theoretical Probability, Springer, vol. 12(3), pages 757-778, July.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:3:d:10.1023_a:1021632016642
    DOI: 10.1023/A:1021632016642
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    References listed on IDEAS

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    1. Meerschaert, Mark M., 1993. "Regular variation and generalized domains of attraction in k," Statistics & Probability Letters, Elsevier, vol. 18(3), pages 233-239, October.
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    Cited by:

    1. Steven J. Sepanski, 2001. "Extreme Values and the Multivariate Compact Law of the Iterated Logarithm," Journal of Theoretical Probability, Springer, vol. 14(4), pages 989-1018, October.

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