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

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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.

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Authors and Affiliations

  1. Department of Mathematics, WonKwang University, Jeonbuk, 570-749, Korea

    Mi-Hwa Ko & Tae-Sung Kim

  2. Department of Computer Science, Howon University, Jeonbuk, 573-718, Korea

    Kwang-Hee Han

Authors
  1. Mi-Hwa Ko
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  2. Tae-Sung Kim
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  3. Kwang-Hee Han
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Correspondence to Tae-Sung Kim.

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Ko, MH., Kim, TS. & Han, KH. A Note on the Almost Sure Convergence for Dependent Random Variables in a Hilbert Space. J Theor Probab 22, 506–513 (2009). https://doi.org/10.1007/s10959-008-0144-z

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  • DOI: https://doi.org/10.1007/s10959-008-0144-z

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