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A two-sided estimate in the Hsu--Robbins--Erdös law of large numbers

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  • Pruss, Alexander R.

Abstract

Let X1, X2, ... be independent identically distributed random variables. Then, Hsu and Robbins (1947) together with Erdös (1949, 1950) have proved that , if and only if E[X21] 0.

Suggested Citation

  • Pruss, Alexander R., 1997. "A two-sided estimate in the Hsu--Robbins--Erdös law of large numbers," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 173-180, October.
    • Handle: RePEc:eee:spapps:v:70:y:1997:i:2:p:173-180
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    Cited by:

    1. Spataru, Aurel, 2011. "Only the first term of some series counts," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1547-1551, October.
    2. A. Spătaru, 2004. "Exact Asymptotics in log log Laws for Random Fields," Journal of Theoretical Probability, Springer, vol. 17(4), pages 943-965, October.
    3. Liu, Weidong & Lin, Zhengyan, 2006. "Precise asymptotics for a new kind of complete moment convergence," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1787-1799, October.
    4. Aurel Spătaru, 1999. "Precise Asymptotics in Spitzer's Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 12(3), pages 811-819, July.
    5. 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.

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