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Almost Sure Central Limit Theory for Self‐Normalized Products of Sums of Partial Sums

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  • Qunying Wu

Abstract

Let X, X1, X2, … be a sequence of independent and identically distributed random variables in the domain of attraction of a normal law. An almost sure limit theorem for the self‐normalized products of sums of partial sums is established.

Suggested Citation

  • Qunying Wu, 2012. "Almost Sure Central Limit Theory for Self‐Normalized Products of Sums of Partial Sums," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:329391
    DOI: 10.1155/2012/329391
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    References listed on IDEAS

    as
    1. Peligrad, Magda & Shao, Qi-Man, 1995. "A note on the almost sure central limit theorem for weakly dependent random variables," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 131-136, February.
    2. Wu, Qunying, 2011. "Almost sure limit theorems for stable distributions," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 662-672, June.
    3. Ibragimov, Ildar & Lifshits, Mikhail, 1998. "On the convergence of generalized moments in almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 343-351, November.
    4. 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.
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