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On Complete Convergence for Weighted Sums of Arrays of Dependent Random Variables

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  • Soo Hak Sung

Abstract

A rate of complete convergence for weighted sums of arrays of rowwise independent random variables was obtained by Sung and Volodin (2011). In this paper, we extend this result to negatively associated and negatively dependent random variables. Similar results for sequences of φ‐mixing and ρ*‐mixing random variables are also obtained. Our results improve and generalize the results of Baek et al. (2008), Kuczmaszewska (2009), and Wang et al. (2010).

Suggested Citation

  • Soo Hak Sung, 2011. "On Complete Convergence for Weighted Sums of Arrays of Dependent Random Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:630583
    DOI: 10.1155/2011/630583
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    References listed on IDEAS

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    1. Qi-Man Shao, 2000. "A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 13(2), pages 343-356, April.
    2. 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.
    3. Ahmed, S. Ejaz & Antonini, Rita Giuliano & Volodin, Andrei, 2002. "On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 185-194, June.
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