Complete and complete integral convergence for weighted sums of arrays of rowwise widely negative dependent random variables under the sub-linear expectations

References

• Bingham, N. H., C. M. Goldie, and J. L. Teugels. 1987. Regular variation. Cambridge University Press. doi:10.1017/CBO9780511721434.
   Google Scholar
• Chen, P., and S. H. Sung. 2016. Complete convergence and strong laws of large numbers for weighted sums of negatively orthant dependent random variables. Acta Mathematica Hungarica 148 (1):83–95. doi:10.1007/s10474-015-0559-9.
   Web of Science ®Google Scholar
• Ding, Y., L. 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.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Kuczmaszewska, A. 2020. Complete convergence for widely acceptable random variables under the sublinear expectation. Journal of Mathematical Analysis and Applications. 484 (1):123662. doi:10.1016/j.jmaa.2019.123662.
   Web of Science ®Google Scholar
• Li, J., and Q. Y. Wu. 2020. Complete integral convergence for arrays of rowwise extended independent random variables under sub-linear expectations. Communications in Statistics - Theory and Methods 49 (22):5613–26. doi:10.1080/03610926.2019.1620954.
   Web of Science ®Google Scholar
• Lin, Y. W., and X. W. Feng. 2020. 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.
   Web of Science ®Google Scholar
• Peng, S. G. 2008a. A new central limit theorem under sublinear expectations. arXiv:0803.2656v1 [Math.PR]
   Google Scholar
• Peng, S. G. 2008b. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stochastic Processes and Their Applications 118 (12):2223–53. doi:10.1016/j.spa.2007.10.015.
   Web of Science ®Google Scholar
• Peng, S. G. 2010. Nonlinear expectations and stochastic calculus under uncertainty. arXiv:1002.4546v1 [Math.PR]
   Google Scholar
• Qiu, D. H., and P. Y. Chen. 2014. Complete moment convergence for i.i.d. random variables. Statistics & Probability Letters 91 (1):76–82. doi:10.1016/j.spl.2014.04.001.
   Web of Science ®Google Scholar
• Wang, X. J., and Y. Wu. 2017. On Complete convergence and complete moment convergence for a class of random variables. Journal of the Korean Mathematical Society 54 (3):877–96. doi:10.4134/JKMS.j160298.
   Web of Science ®Google Scholar
• Wu, Y., X. J. Wang, and A. Rosalsky. 2018. Complete moment convergence for arrays of rowwise widely orthant dependent random variables. Acta Mathematica Sinica, English Series 34 (10):1531–48. doi:10.1007/s10114-018-7173-z.
   Web of Science ®Google Scholar
• Wu, Y., X. J. Wang, and L. X. Zhang. 2018. On the asymptotic approximation of inverse moment under sub-linear expectations. Journal of Mathematical Analysis and Applications 468 (1):182–96. doi:10.1016/j.jmaa.2018.08.010.
   Web of Science ®Google Scholar
• Zhang, L. X. 2015. Donsker’s invariance principle under the sub-linear expectation with an application to Chung’s law of the iterated logarithm. Communications in Mathematics and Statistics 3 (2):187–214. doi:10.1007/s40304-015-0055-0.
   Web of Science ®Google Scholar
• Zhang, L. X. 2016a. Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations. arXiv:1608.00710v1 [Math.PR]
   Google Scholar
• Zhang, L. X. 2016b. Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications. Science China Mathematics 59 (4):751–68. doi:10.1007/s11425-015-5105-2.
   Web of Science ®Google Scholar
• 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):261. doi:10.1186/s13660-017-1538-1.
   PubMed Web of Science ®Google Scholar