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On the strong law of large numbers for identically distributed random variables irrespective of their joint distributions

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  • Rosalsky, Andrew
  • Stoica, George

Abstract

For a sequence of identically distributed random variables {Xn,n>=1} with partial sums and a sequence of positive constants {bn,n>=1} with bn[NE pointing arrow][infinity], conditions are provided under which the strong law of large numbers Sn/bn-->0 almost surely holds irrespective of the joint distributions of the {Xn,n>=1}. It is not assumed that EX1

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:17-18:p:1265-1270
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    References listed on IDEAS

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    1. 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.
    2. Rosalsky, Andrew, 1987. "A strong law for a set-indexed partial sum process with applications to exchangeable and stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 277-287.
    3. Maller, R. A., 1980. "On the law of large numbers for stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 10(1), pages 65-73, June.
    4. 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.
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    Cited by:

    1. Chen, Pingyan & Sung, Soo Hak, 2016. "On the strong laws of large numbers for weighted sums of random variables," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 87-93.

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