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A supplement to the complete convergence

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  • Weidong, Liu
  • Zhengyan, Lin

Abstract

Let X,X1,X2,... be independent identically distributed random variables. Then, Baum and Katz [1965. Convergence rates in the law of large numbers. Trans. Amer. Math. Soc. 120, 108-123] proved that for p>1,if and only if and . We prove thatif and only if and is slowly varying as x-->[infinity].

Suggested Citation

  • Weidong, Liu & Zhengyan, Lin, 2006. "A supplement to the complete convergence," Statistics & Probability Letters, Elsevier, vol. 76(7), pages 748-754, April.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:7:p:748-754
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