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On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes

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  • Ahmed, S. Ejaz
  • Antonini, Rita Giuliano
  • Volodin, Andrei

Abstract

We obtain complete convergence results for arrays of rowwise independent Banach space valued random elements. In the main result no assumptions are made concerning the geometry of the underlying Banach space. As corollaries we obtain a result on complete convergence in stable type p Banach spaces and on the complete convergence of moving average processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:58:y:2002:i:2:p:185-194
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    References listed on IDEAS

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    1. Li, Deli & Bhaskara Rao, M. & Wang, Xiangchen, 1992. "Complete convergence of moving average processes," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 111-114, May.
    2. Burton, Robert M. & Dehling, Herold, 1990. "Large deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 9(5), pages 397-401, May.
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    Cited by:

    1. Berkes, István & Weber, Michel, 2007. "On complete convergence of triangular arrays of independent random variables," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 952-963, June.
    2. Kuczmaszewska, Anna, 2007. "On complete convergence for arrays of rowwise dependent random variables," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1050-1060, June.
    3. Tómács, Tibor, 2005. "Convergence rates in the law of large numbers for arrays of Banach space valued random elements," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 59-69, April.
    4. Tae-Sung Kim & Mi-Hwa Ko, 2008. "On the Complete Convergence of Moving Average Process with Banach Space Valued Random Elements," Journal of Theoretical Probability, Springer, vol. 21(2), pages 431-436, June.
    5. Ming Le Guo, 2012. "Complete Moment Convergence of Weighted Sums for Arrays of Rowwise -Mixing Random Variables," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-13, September.
    6. Jong-Il Baek & Sung-Tae Park, 2010. "RETRACTED ARTICLE: Convergence of Weighted Sums for Arrays of Negatively Dependent Random Variables and Its Applications," Journal of Theoretical Probability, Springer, vol. 23(2), pages 362-377, June.

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