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On almost sure limit theorems for positively dependent random variables

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  • Matula, Przemyslaw

Abstract

In this note, we prove an almost sure limit theorem for pairwise quadrant-dependent random variables. From the main result, we obtain the Glivenko-Cantelli lemma for pairwise PQD and the almost sure central limit theorem for i.i.d. random variables.

Suggested Citation

  • Matula, Przemyslaw, 2005. "On almost sure limit theorems for positively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 59-66, August.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:1:p:59-66
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    References listed on IDEAS

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    1. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    2. Etemadi, N., 1983. "Stability of sums of weighted nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 361-365, June.
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    Cited by:

    1. H. Jabbari, 2013. "On almost sure convergence for weighted sums of pairwise negatively quadrant dependent random variables," Statistical Papers, Springer, vol. 54(3), pages 765-772, August.

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