IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i16p3494-d1216297.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/16/3494/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/16/3494/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    3. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Feng, Chunrong & Wu, Panyu & Zhao, Huaizhong, 2020. "Ergodicity of invariant capacities," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5037-5059.
    2. Ludwig, Alexander & Zimper, Alexander, 2014. "Biased Bayesian learning with an application to the risk-free rate puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 79-97.
    3. repec:rza:wpaper:240 is not listed on IDEAS
    4. Philippe, Fabrice, 2000. "Cumulative prospect theory and imprecise risk," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 237-263, November.
    5. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    6. Anna Kuczmaszewska, 2025. "Quantiles under the sub-linear expectations," Statistical Papers, Springer, vol. 66(4), pages 1-15, June.
    7. Wang, Tan, 2003. "Conditional preferences and updating," Journal of Economic Theory, Elsevier, vol. 108(2), pages 286-321, February.
    8. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    9. Alexander Zimper & Alexander Ludwig, 2009. "On attitude polarization under Bayesian learning with non-additive beliefs," Journal of Risk and Uncertainty, Springer, vol. 39(2), pages 181-212, October.
    10. Ralph W. Bailey & Jürgen Eichberger & David Kelsey, 2005. "Ambiguity and Public Good Provision in Large Societies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(5), pages 741-759, December.
    11. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    12. Diecidue, Enrico & Wakker, Peter P, 2001. "On the Intuition of Rank-Dependent Utility," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 281-298, November.
    13. Kiyohiko G. Nishimura & Hiroyuki Ozaki, 2001. "Search under the Knightian Uncertainty," CIRJE F-Series CIRJE-F-112, CIRJE, Faculty of Economics, University of Tokyo.
    14. Hill, Brian, 2010. "An additively separable representation in the Savage framework," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2044-2054, September.
    15. Criens, David & Niemann, Lars, 2024. "A class of multidimensional nonlinear diffusions with the Feller property," Statistics & Probability Letters, Elsevier, vol. 208(C).
    16. Marcello Basili & Stefano Dalle Mura, 2004. "Ambiguity and macroeconomics:a rationale for price stickiness," Department of Economics University of Siena 428, Department of Economics, University of Siena.
    17. Andreas Lehnert & Wayne Passmore, 1999. "Pricing systemic crises: monetary and fiscal policy when savers are uncertain," Finance and Economics Discussion Series 1999-33, Board of Governors of the Federal Reserve System (U.S.).
    18. Mira Frick & Ryota Iijima & Tomasz Strzalecki, 2019. "Dynamic Random Utility," Econometrica, Econometric Society, vol. 87(6), pages 1941-2002, November.
    19. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    20. Junyi Chai & Zhiquan Weng & Wenbin Liu, 2021. "Behavioral Decision Making in Normative and Descriptive Views: A Critical Review of Literature," JRFM, MDPI, vol. 14(10), pages 1-14, October.
    21. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3494-:d:1216297. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.