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On Complete Convergence and Strong Law for Weighted Sums of i.i.d. Random Variables

Author

Listed:
  • Pingyan Chen
  • Xiaofang Ma
  • Soo Hak Sung

Abstract

We improve and generalize the result of Stout (1974, Theorem 4.1.3). In particular, the sharp moment conditions are obtained and some well‐known results can be obtained as special cases of the main result. The method of the proof is completely different from that in Stout. We also improve and generalize Li et al. (1995) strong law for weighted sums of i.i.d. random variables.

Suggested Citation

  • Pingyan Chen & Xiaofang Ma & Soo Hak Sung, 2014. "On Complete Convergence and Strong Law for Weighted Sums of i.i.d. Random Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:251435
    DOI: 10.1155/2014/251435
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    References listed on IDEAS

    as
    1. Bing-Yi Jing & Han-Ying Liang, 2008. "Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables," Journal of Theoretical Probability, Springer, vol. 21(4), pages 890-909, December.
    2. Soo Sung, 2012. "Complete convergence for weighted sums of negatively dependent random variables," Statistical Papers, Springer, vol. 53(1), pages 73-82, February.
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    Cited by:

    1. Miaomiao Wang & Shunping Zheng & Xuejun Wang, 2025. "Equivalent conditions of complete moment convergence for randomly weighted sums of random variables and some applications with random design," Statistical Papers, Springer, vol. 66(2), pages 1-33, February.

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