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Extreme Values and the Multivariate Compact Law of the Iterated Logarithm

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  • Steven J. Sepanski

    (Saginaw Valley State University)

Abstract

For a sequence of independent identically distributed Euclidean random vectors, we prove a compact Law of the iterated logarithm when finitely many maximal terms are omitted from the partial sum. With probability one, the limiting cluster set of the appropriately operator normed partial sums is the closed unit Euclidean ball. The result is proved under the hypotheses that the random vectors belong to the Generalized Domain of Attraction of the multivariate Gaussian law and satisfy a mild integrability condition. The integrability condition characterizes how many maximal terms must be omitted from the partial sum sequence.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:4:d:10.1023_a:1017576903851
    DOI: 10.1023/A:1017576903851
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    References listed on IDEAS

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    1. 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.
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