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A Note on the Almost Sure Convergence for Dependent Random Variables in a Hilbert Space

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  • Mi-Hwa Ko

    (WonKwang University)

  • Tae-Sung Kim

    (WonKwang University)

  • Kwang-Hee Han

    (Howon University)

Abstract

We obtain the almost sure convergence for sequences of H-valued random variables which are either associated or negatively associated. Our results extend the results of Birkel (Stat. Probab. Lett. 7:17–20, 1989) and Matula (Stat. Probab. Lett. 15:209–213, 1992) to a Hilbert space.

Suggested Citation

  • Mi-Hwa Ko & Tae-Sung Kim & Kwang-Hee Han, 2009. "A Note on the Almost Sure Convergence for Dependent Random Variables in a Hilbert Space," Journal of Theoretical Probability, Springer, vol. 22(2), pages 506-513, June.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:2:d:10.1007_s10959-008-0144-z
    DOI: 10.1007/s10959-008-0144-z
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    References listed on IDEAS

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    1. Matula, Przemyslaw, 1992. "A note on the almost sure convergence of sums of negatively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 209-213, October.
    2. Burton, Robert M. & Dabrowski, AndréRobert & Dehling, Herold, 1986. "An invariance principle for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 301-306, December.
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    Cited by:

    1. Chang, Mengmeng & Miao, Yu, 2023. "Generalized weak laws of large numbers in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 197(C).

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