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On the Strong Convergence and Complete Convergence for Pairwise NQD Random Variables

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  • Aiting Shen
  • Ying Zhang
  • Andrei Volodin

Abstract

Let {an, n ≥ 1} be a sequence of positive constants with an/n↑ and let {X, Xn, n ≥ 1} be a sequence of pairwise negatively quadrant dependent random variables. The complete convergence for pairwise negatively quadrant dependent random variables is studied under mild condition. In addition, the strong laws of large numbers for identically distributed pairwise negatively quadrant dependent random variables are established, which are equivalent to the mild condition ∑n=1∞PX>an

Suggested Citation

  • Aiting Shen & Ying Zhang & Andrei Volodin, 2014. "On the Strong Convergence and Complete Convergence for Pairwise NQD Random Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:949608
    DOI: 10.1155/2014/949608
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    References listed on IDEAS

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    1. Sung, Soo Hak, 2013. "On the strong law of large numbers for pairwise i.i.d. random variables with general moment conditions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1963-1968.
    2. Wang, Xuejun & Hu, Shuhe & Shen, Yan & Ling, Nengxiang, 2008. "Strong law of large numbers and growth rate for a class of random variable sequences," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3330-3337, December.
    3. Kruglov, Victor M., 2008. "A strong law of large numbers for pairwise independent identically distributed random variables with infinite means," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 890-895, May.
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