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Mean convergence for the maximum of weighted sums of negatively associated random variables under Gut’s condition

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  • Thành, Lê Vǎn

Abstract

Gut (2004) provided necessary and sufficient conditions for the weak law of large numbers with regularly varying norming sequences. This paper shows that Gut’s conditions are also necessary and sufficient for a mean convergence result for the maximum of the weighted sums. A complement to the main result in Boukhari (2022) is also presented. The sharpness of the main theorems is illustrated by three examples.

Suggested Citation

  • Thành, Lê Vǎn, 2026. "Mean convergence for the maximum of weighted sums of negatively associated random variables under Gut’s condition," Statistics & Probability Letters, Elsevier, vol. 230(C).
    • Handle: RePEc:eee:stapro:v:230:y:2026:i:c:s0167715225002573
    DOI: 10.1016/j.spl.2025.110612
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    References listed on IDEAS

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    1. Qi-Man Shao, 2000. "A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 13(2), pages 343-356, April.
    2. 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.
    3. Rosalsky, Andrew & Thành, Lê Vǎn, 2021. "A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 178(C).
    4. Stoica, George & Li, Deli, 2025. "Complete convergence with regularly varying moments and norming constants," Statistics & Probability Letters, Elsevier, vol. 223(C).
    5. A. Gut, 2004. "An Extension of the Kolmogorov–Feller Weak Law of Large Numbers with an Application to the St. Petersburg Game," Journal of Theoretical Probability, Springer, vol. 17(3), pages 769-779, July.
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