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The Law of the Iterated Logarithm for m-Dependent Banach Space Valued Random Variables

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  • Xia Chen

    (Case Western Reserve University)

Abstract

A theorem on the law of the iterated logarithm is established for m-dependent B-valued random variables. The conditions in our theorem match their independent analogues and appear as necessary or minimal for the results. According to an example given in the paper, the situation we face is much different from the finite dimensional case and therefore, so is the way we solve the problems.

Suggested Citation

  • Xia Chen, 1997. "The Law of the Iterated Logarithm for m-Dependent Banach Space Valued Random Variables," Journal of Theoretical Probability, Springer, vol. 10(3), pages 695-732, July.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:3:d:10.1023_a:1022605812085
    DOI: 10.1023/A:1022605812085
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