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The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences under Sublinear Expectation

Author

Listed:
  • Shuxia Guo

    (School of Mathematics, Shandong University, Jinan 250100, China)

  • Zhe Meng

    (Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China)

Abstract

In this paper we study the Marcinkiewicz–Zygmund-type strong law of large numbers with general normalizing sequences under sublinear expectation. Specifically, we establish complete convergence in the Marcinkiewicz–Zygmund-type strong law of large numbers for sequences of negatively dependent and identically distributed random variables under certain moment conditions. We also give results for sequences of independent and identically distributed random variables. The moment conditions in this paper are based on a class of slowly varying functions that satisfy some convergence properties. Moreover, some special examples and comparisons to existing results are also given.

Suggested Citation

  • Shuxia Guo & Zhe Meng, 2023. "The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences under Sublinear Expectation," Mathematics, MDPI, vol. 11(23), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4734-:d:1285748
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    References listed on IDEAS

    as
    1. Zhouting Zhan & Qunying Wu, 2022. "Strong laws of large numbers for weighted sums of extended negatively dependent random variables under sub-linear expectations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(5), pages 1197-1216, March.
    2. Yiwei Lin & Xinwei Feng, 2020. "Complete convergence and strong law of large numbers for arrays of random variables under sublinear expectations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(23), pages 5866-5882, December.
    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. Bai, Z. D. & Cheng, Philip E., 2000. "Marcinkiewicz strong laws for linear statistics," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 105-112, January.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    6. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    7. Soo Hak Sung, 2014. "Marcinkiewicz–Zygmund Type Strong Law of Large Numbers for Pairwise i.i.d. Random Variables," Journal of Theoretical Probability, Springer, vol. 27(1), pages 96-106, March.
    8. Fengxiang Feng & Haiwu Huang, 2021. "Strong convergence for weighted sums of END random variables under the sub-linear expectations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(22), pages 7885-7896, September.
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