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A strong law of large numbers for nonnegative random variables and applications

Author

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  • Chen, Pingyan
  • Sung, Soo Hak

Abstract

For a sequence of nonnegative random variables {Xn,n≥1} with finite means and partial sums Sn=∑i=1nXi,n≥1, and a sequence of positive numbers {bn,n≥1} with bn↑∞, sufficient conditions are given under which (Sn−ESn)/bn→0 almost surely. Our result generalizes the strong law of large numbers obtained by Korchevsky (2015). Some applications for dependent random variables are also provided.

Suggested Citation

  • Chen, Pingyan & Sung, Soo Hak, 2016. "A strong law of large numbers for nonnegative random variables and applications," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 80-86.
    • Handle: RePEc:eee:stapro:v:118:y:2016:i:c:p:80-86
    DOI: 10.1016/j.spl.2016.06.017
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    References listed on IDEAS

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    1. Etemadi, N., 1983. "Stability of sums of weighted nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 361-365, June.
    2. Korchevsky, Valery, 2015. "A generalization of the Petrov strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 102-108.
    3. H. Jabbari, 2013. "On almost sure convergence for weighted sums of pairwise negatively quadrant dependent random variables," Statistical Papers, Springer, vol. 54(3), pages 765-772, August.
    4. Etemadi, Nasrollah, 1983. "On the laws of large numbers for nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 187-193, March.
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    Citations

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    Cited by:

    1. Lita da Silva, João, 2018. "Strong laws of large numbers for pairwise quadrant dependent random variables," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 349-358.
    2. Quang, Nguyen Van & Son, Do The & Son, Le Hong, 2017. "The strong laws of large numbers for positive measurable operators and applications," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 110-120.

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