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Cesàro α-Integrability and Laws of Large Numbers-II

Author

Listed:
  • T. K. Chandra

    (Indian Statistical Institute)

  • A. Goswami

    (Indian Statistical Institute)

Abstract

For a sequence of random variables, a new set of properties called Cesàro α-Integrability and Strong Cesàro α-Integrability was recently introduced in an earlier paper and these properties were used to prove several new laws of large numbers, namely both Strong and Weak Laws of Large Numbers for pairwise-independent random variables as well as WLLN for some dependent sequences of random variables. In this paper, a set of weaker conditions called Residual Cesàro α-Integrability and Strong Residual Cesàro α-Integrability are introduced and significant improvements over earlier results are obtained. In addition, new results on L p -convergence, for 0

Suggested Citation

  • T. K. Chandra & A. Goswami, 2006. "Cesàro α-Integrability and Laws of Large Numbers-II," Journal of Theoretical Probability, Springer, vol. 19(4), pages 789-816, December.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:4:d:10.1007_s10959-006-0038-x
    DOI: 10.1007/s10959-006-0038-x
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    References listed on IDEAS

    as
    1. T. K. Chandra & A. Goswami, 2003. "Cesàro α-Integrability and Laws of Large Numbers I," Journal of Theoretical Probability, Springer, vol. 16(3), pages 655-669, July.
    2. R. L. Taylor & R. F. Patterson & A. Bozorgnia, 2001. "Weak laws of large numbers for arrays of rowwise negatively dependent random variables," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-10, January.
    3. Birkel, Thomas, 1992. "Laws of large numbers under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 14(5), pages 355-362, July.
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