78
Views
1
CrossRef citations to date
0
Altmetric
Research Articles

Complete convergence and complete integral convergence for randomly weighted sums under the sublinear expectations

&
Pages 4790-4804 | Received 23 Jun 2022, Accepted 09 Mar 2023, Published online: 03 Apr 2023

References

  • Chow, Y. S. 1988. On the rate of moment convergence of sample sums and extremes. Bulletin of the Institute of Mathematics Academia Sinica 16 (3):177–201.
  • Ding, Y., Y. Wu, S. L. Ma, X. R. Tao, and X. J. Wang. 2017. Complete convergence and complete moment convergence for widely orthant-dependent random variables. Communications in Statistics-Theory and Methods 46 (16):8278–94. doi: 10.1080/03610926.2016.1177085.
  • Feng, F. X., D. C. Wang, Q. Y. Wu, and H. W. Huang. 2021. Complete and complete moment convergence for weighted sums of arrays of rowwise negatively dependent random variables under the sub-linear expectations. Communications in Statistics- Theory and Methods 50 (3):594–608. doi: 10.1080/03610926.2019.1639747.
  • Hsu, P. L., and H. Robbins. 1947. Complete convergence and the law of large numbers. Proceedings of the National Academy of Sciences of the United States of America 33 (2):25–31. doi: 10.1073/pnas.33.2.25.
  • Liang, H. Y., D. L. Li, and A. Rosalsky. 2010. Complete moment and integral convergence for sums of negatively associated random variables. Acta Mathematica Sinica-English Series 26 (3):419–32. doi: 10.1007/s10114-010-8177-5.
  • Liang, Z. W, and Q. Y. Wu. 2019. Theorems of complete convergence and complete integral convergence for END random variables under sub-linear expectations. Journal of Inequalities and Applications 2019 (1):1–17. doi: 10.1186/s13660-019-2064-0.
  • Liang, Z. W, and Q. Y. Wu. 2021. Complete Choquet integral convergence under sub-linear expectations. Advances in Mathematics (China) 50 (4):629–40. doi: 10.11845/sxjz.2020023b.
  • Lin, Y. W, and X. W. Feng. 2019. Complete convergence and strong law of large numbers for arrays of random variables under sublinear expectations. Communications in Statistics-Theory and Methods 49 (23):5866–82. doi: 10.1080/03610926.2019.1625924.
  • Lu, D. W, and Y. Meng. 2021. Complete and complete integral convergence for weighted sums of arrays of rowwise widely negative dependent random variables under the sub-linear expectations. Communications in Statistics-Theory and Methods: 1–14. doi: 10.1080/03610926.2021.1934027.
  • Lu, D. W, and J. L. Wang. 2021. Complete convergence and complete moment convergence for maximal randomly weighted sums of widely orthant-dependent random variables with applications. Communications in Statistics-Theory and Methods 50 (4):763–91. doi: 10.1080/03610926.2019.1640879.
  • Peng, S. G. 1997. Backward SDE and related g-expectation. Pitman research notes in mathematics series 364:141–59.
  • Peng, S. G. 2007. G-expectation, G-Brownian motion and related stochastic calculus of Itô type. Stochastic Analysis and Applications 2 (4):541–67.
  • Peng, S. G. 2008a. A new central limit theorem under sublinear expectations. ArXiv:0803.2656v1 [math.PR].
  • Peng, S. G. 2008b. Multi-dimensional G-brownian motion and related stochastic calculus under gexpectation. 118:2223–53. doi: 10.1016/j.spa.2007.10.015.
  • Shen, A. T., M. X. Xue, and W. J. Wang. 2017. Complete convergence for weighted sums of extended negatively dependent random variables. Communications in Statistics-Theory and Methods 46 (3): 1433–44. doi: 10.1080/03610926.2015.1019147.
  • Wang, X. J., S. H. Hu, and W. Z. Yang. 2012. Complete convergence for arrays of rowwise negatively orthant dependent random variables. Revista de la Real Academia de Ciencias Exactas Fisicas. Naturales Serie A-Matematics 106 (2):235–45. doi: 10.1007/s13398-011-0048-0.
  • Wu, Q. Y, and Y. Y. Jiang. 2016. Complete convergence and complete moment convergence for negatively associated sequences of random variables. Journal of Inequalities and Applications 2016 (1):1–10. doi: 10.1186/s13660-016-1107-z.
  • Wu, Q. Y, and Y. Y. Jiang. 2020. Complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations. Filomat 34 (4):1093–104. doi: 10.2298/FIL2004093W.
  • Wu, Y. F., J. Y. Peng, and T. C. Hu. 2015. Limiting behaviour for arrays of row-wise END random variables under conditions of h-integrability. Stochastics-An International Journal of Probability and Stochastic Processes 87 (3):409–23. doi: 10.1080/17442508.2014.959951.
  • Zhang, L. X. 2016. Exponential inequalities under sub-linear expectations with applications to laws of the iterated logarithm. Science China Mathematics 59 (12):2503–26. doi: 10.1007/s11425-016-0079-1.
  • Zhang, L. X. 2022. Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations. Acta Mathematica Scientia 42 (2):467–90. doi: 10.1007/s10473-022-0203-z.
  • Zhong, H. Y, and Q. Y. Wu. 2017. Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation. Journal of Inequalities and Applications 2017 (1):1–14. doi: 10.1186/s13660-017-1538-1.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.