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Some strong limit theorems for -mixing sequences of random variables

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  • Wu, Qunying
  • Jiang, Yuanying

Abstract

In this paper, we study the almost sure convergence for -mixing sequences of random variables. As a result, the authors improve the corresponding results of Yang [Yang, Shanchao, 1998. Some moment inequalities for partial sums of random variables and their applications. Chinese Sci. Bull. 43 (17), 1823-1827], Gan [Gan, Shixin, 2004. Almost sure convergence for -mixing random variable sequences. Statist. Probab. Lett. 67, 289-298], and Wu [Wu, Qunying, 2001. Some convergence properties for -mixing sequences. J. Engng. Math. 18 (3), 58-64 (in Chinese)]. We extend the classical Khintchine-Kolmogorov convergence theorem, the Marcinkiewicz strong law of large numbers, and the three series theorem for independent sequences of random variables to -mixing sequences of random variables without necessarily adding any extra conditions.

Suggested Citation

  • Wu, Qunying & Jiang, Yuanying, 2008. "Some strong limit theorems for -mixing sequences of random variables," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 1017-1023, June.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:8:p:1017-1023
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    1. Shixin, Gan, 2004. "Almost sure convergence for -mixing random variable sequences," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 289-298, May.
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    Cited by:

    1. Soo Sung, 2013. "On the strong convergence for weighted sums of ρ * -mixing random variables," Statistical Papers, Springer, vol. 54(3), pages 773-781, August.

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