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On the almost certain limiting behavior of normed sums of identically distributed positive random variables

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  • Rosalsky, Andrew

Abstract

Consider a sequence of identically distributed positive random variables {Xn, n [greater-or-equal, slanted] 1} with partial sums Sn = [summation operator]nj = 1, Xj, n [greater-or-equal, slanted] 1, and let {bn & 0, n [greater-or-equal, slanted] 1} be a sequence of norming constants. The almost certain limiting behavior of the normed sums Sn/bn is investigated irrespective of the joint distributions of the {Xn, n [greater-or-equal, slanted] 1}. Some open problems are also formulated. The current investigation was inspired by that of Smit and Vervaat (1983) on the convergence of series of nonnegative random variables irrespective of the joint distributions of the random variables.

Suggested Citation

  • Rosalsky, Andrew, 1993. "On the almost certain limiting behavior of normed sums of identically distributed positive random variables," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 65-70, January.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:1:p:65-70
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    Cited by:

    1. Rosalsky, Andrew & Stoica, George, 2010. "On the strong law of large numbers for identically distributed random variables irrespective of their joint distributions," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1265-1270, September.
    2. Klesov, Oleg & Rosalsky, Andrew & Volodin, Andrei I., 2005. "On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 193-202, February.
    3. Fakhreddine Boukhari, 2022. "On a Weak Law of Large Numbers with Regularly Varying Normalizing Sequences," Journal of Theoretical Probability, Springer, vol. 35(3), pages 2068-2079, September.
    4. Rosalsky, Andrew & Sreehari, M., 1998. "On the limiting behavior of randomly weighted partial sums," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 403-410, November.

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