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Strong law of large numbers and growth rate for a class of random variable sequences

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  • Wang, Xuejun
  • Hu, Shuhe
  • Shen, Yan
  • Ling, Nengxiang

Abstract

Fazekas and Klesov [Fazekas, I., Klesov, O., 2000. A general approach to the strong law of large numbers. Theory of Probability and its Applications 45, 436-449] established a Hájek-Rényi-type maximal inequality and obtained a strong law of large numbers (SLLN) for the sums of random variables. Hu and Hu [Hu Shuhe, Hu Ming, 2006. A general approach rate to the strong law of large numbers. Statistics and Probability Letters 76, 843-851] obtained the SLLN and the growth rate for a sequence of random variables by using the Hájek-Rényi-type maximal inequality. This paper obtains some new results of the SLLN and growth rate for strongly positive dependent stochastic sequences, PA sequences, -mixing sequences, -mixing sequences and pairwise negatively quadrant dependent sequences.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3330-3337
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    References listed on IDEAS

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    1. Wang, Jianfeng, 2004. "Maximal inequalities for associated random variables and demimartingales," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 347-354, February.
    2. Christofides, Tasos C., 2000. "Maximal inequalities for demimartingales and a strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 357-363, December.
    3. Shuhe, Hu & Ming, Hu, 2006. "A general approach rate to the strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 843-851, April.
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