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Equivalent Conditions of Complete p-th Moment Convergence for Weighted Sum of ND Random Variables under Sublinear Expectation Space

Author

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  • Peiyu Sun

    (School of Mathematics, Jilin University, Changchun 130012, China
    School of Mathematics and Statistics, Beihua University, Jilin 132013, China)

  • Dehui Wang

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110031, China)

  • Xili Tan

    (School of Mathematics and Statistics, Beihua University, Jilin 132013, China)

Abstract

We investigate the complete convergence for weighted sums of sequences of negative dependence (ND) random variables and p-th moment convergence for weighted sums of sequences of ND random variables under sublinear expectation space. Using moment inequality and truncation methods, we prove the equivalent conditions of complete convergence for weighted sums of sequences of ND random variables and p-th moment convergence for weighted sums of sequences of ND random variables under sublinear expectation space.

Suggested Citation

  • Peiyu Sun & Dehui Wang & Xili Tan, 2023. "Equivalent Conditions of Complete p-th Moment Convergence for Weighted Sum of ND Random Variables under Sublinear Expectation Space," Mathematics, MDPI, vol. 11(16), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3494-:d:1216297
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    References listed on IDEAS

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    1. Zengjing Chen & Xinwei Feng, 2016. "Large deviation for negatively dependent random variables under sublinear expectation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 400-412, January.
    2. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    3. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    4. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    5. Wei Liu & Yong Zhang, 2023. "Large deviation principle for linear processes generated by real stationary sequences under the sub-linear expectation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(16), pages 5727-5741, August.
    6. 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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