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A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers

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  • Rosalsky, Andrew
  • Thành, Lê Vǎn

Abstract

In this correspondence, we present new results concerning the concept of stochastic domination and apply them to obtain new results on uniform integrability and on the strong law of large numbers for sequences of pairwise independent random variables. Our result on the strong law of large numbers extends a result of Chen, Bai, and Sung (2014). The sharpness of the results is illustrated by three examples.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:178:y:2021:i:c:s0167715221001437
    DOI: 10.1016/j.spl.2021.109181
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    References listed on IDEAS

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    1. Wei, Duan & Taylor, R. L., 1978. "Convergence of weighted sums of tight random elements," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 282-294, June.
    2. Hu, Tien-Chung & Rosalsky, Andrew, 2011. "A note on the de La Vallée Poussin criterion for uniform integrability," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 169-174, January.
    3. Chandra, Tapas Kumar, 2015. "de La Vallée Poussin’s theorem, uniform integrability, tightness and moments," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 136-141.
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    Citations

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    Cited by:

    1. Chang, Mengmeng & Miao, Yu, 2023. "Generalized weak laws of large numbers in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 197(C).
    2. Lê Vǎn Thành, 2023. "On a new concept of stochastic domination and the laws of large numbers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 74-106, March.
    3. Thành, Lê Vǎn, 2024. "On Rio’s proof of limit theorems for dependent random fields," Stochastic Processes and their Applications, Elsevier, vol. 171(C).

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