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A Refinement of the Kolmogorov–Marcinkiewicz–Zygmund Strong Law of Large Numbers

Author

Listed:
  • Deli Li

    (Lakehead University)

  • Yongcheng Qi

    (University of Minnesota Duluth)

  • Andrew Rosalsky

    (University of Florida)

Abstract

Let {X n ; n≥1} be a sequence of independent copies of a real-valued random variable X and set S n =X 1+⋅⋅⋅+X n , n≥1. This paper is devoted to a refinement of the classical Kolmogorov–Marcinkiewicz–Zygmund strong law of large numbers. We show that for 0 t)\,dt}{n} t)\,dt t)

Suggested Citation

  • Deli Li & Yongcheng Qi & Andrew Rosalsky, 2011. "A Refinement of the Kolmogorov–Marcinkiewicz–Zygmund Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 24(4), pages 1130-1156, December.
    • Handle: RePEc:spr:jotpro:v:24:y:2011:i:4:d:10.1007_s10959-010-0308-5
    DOI: 10.1007/s10959-010-0308-5
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    References listed on IDEAS

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    1. Florian Hechner & Bernard Heinkel, 2010. "The Marcinkiewicz–Zygmund LLN in Banach Spaces: A Generalized Martingale Approach," Journal of Theoretical Probability, Springer, vol. 23(2), pages 509-522, June.
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    Cited by:

    1. Michael J. Klass & Deli Li & Andrew Rosalsky, 2022. "Divergence Criterion for a Class of Random Series Related to the Partial Sums of I.I.D. Random Variables," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1556-1573, September.
    2. Lê Vǎn Thành, 2023. "On the (p,q)$(p,q)$‐type strong law of large numbers for sequences of independent random variables," Mathematische Nachrichten, Wiley Blackwell, vol. 296(1), pages 402-423, January.

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    2. Michael J. Klass & Deli Li & Andrew Rosalsky, 2022. "Divergence Criterion for a Class of Random Series Related to the Partial Sums of I.I.D. Random Variables," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1556-1573, September.
    3. Lê Vǎn Thành, 2023. "On the (p,q)$(p,q)$‐type strong law of large numbers for sequences of independent random variables," Mathematische Nachrichten, Wiley Blackwell, vol. 296(1), pages 402-423, January.

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