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On the strong convergence for weighted sums of ρ * -mixing random variables

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  • Soo Sung

Abstract

A complete convergence result is obtained for weighted sums of identically distributed ρ * -mixing random variables with E|X 1 | α log(1 + |X 1 |) > ∞ for some 0 > α ≤ 2. This result partially extends the result of Sung (Stat Papers 52: 447–454, 2011 ) for negatively associated random variables to ρ * -mixing random variables. It also settles the open problem posed by Zhou et al. (J Inequal Appl, 2011 , doi: 10.1155/2011/157816 ). Copyright Springer-Verlag 2013

Suggested Citation

  • Soo Sung, 2013. "On the strong convergence for weighted sums of ρ * -mixing random variables," Statistical Papers, Springer, vol. 54(3), pages 773-781, August.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:773-781
    DOI: 10.1007/s00362-012-0461-2
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    References listed on IDEAS

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    1. Kuczmaszewska, Anna, 2007. "On complete convergence for arrays of rowwise dependent random variables," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1050-1060, June.
    2. Wu, Qunying & Jiang, Yuanying, 2008. "Some strong limit theorems for -mixing sequences of random variables," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 1017-1023, June.
    3. Soo Sung, 2011. "On the strong convergence for weighted sums of random variables," Statistical Papers, Springer, vol. 52(2), pages 447-454, May.
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