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Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of ρ~‐Mixing Random Variables

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  • Chongfeng Lan

Abstract

The equivalent conditions of complete convergence are established for weighted sums of ρ~‐mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz‐Zygmund type strong law of large numbers for sequence of ρ~‐mixing random variables is obtained.

Suggested Citation

  • Chongfeng Lan, 2014. "Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of ρ~‐Mixing Random Variables," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:612140
    DOI: 10.1155/2014/612140
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    References listed on IDEAS

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    1. Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
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    3. 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.
    4. Magda Peligrad & Allan Gut, 1999. "Almost-Sure Results for a Class of Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 12(1), pages 87-104, January.
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