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

References

• Chen, P. Y., and D. C. Wang. 2010. Complete moment convergence for sequence of identically distributed φ-mixing random variables. Acta Mathematica Sinica, English Series 26 (4):679–90. doi:10.1007/s10114-010-7625-6.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• Fang, X., S. G. Peng, Q. M. Shao, and Y. S. Song. 2019. Limit theorems with rate of convergence under sublinear expectations. Bernoulli 25 (4A):2564–96. doi:10.3150/18-BEJ1063.
   Web of Science ®Google Scholar
• 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.
   PubMed Web of Science ®Google Scholar
• Hu, Z. C., and L. Zhou. 2015. Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations. Acta Mathematica Sinica, English Series 31 (2):305–18. doi:10.1007/s10114-015-3212-1.
   Web of Science ®Google Scholar
• 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.
   PubMed 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
• Li, J., and Q. Y. Wu. 2020. Complete integral convergence for arrays of row-wise 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
• Li, S. Y., and Q. Y. Wu 2021. Complete integration convergence for arrays of rowwise extended negatively dependent random variables under the sub-linear expectations. AIMS Mathematics 6 (11):12166–81. doi:10.3934/math.2021706.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Peng, S. G. 2006. G-expectation, G-Brownian motion and related stochastic calculus of Itô type. Stochastic Analysis and Applications 2 (4):541–67. doi:10.1007/978-3-540-70847-6_25.
   Google Scholar
• Peng, S. G. 2008. 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
• Qiu, D. H., and P. Y. Chen. 2016. Convergence for weighted sums of widely orthant dependent random variables. Communications in Statistics - Theory and Methods 45 (15):4445–53. doi:10.1080/03610926.2014.921304.
   Web of Science ®Google Scholar
• Wu, Q. Y. 2012. A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables. Journal of Inequalities and Applications 2012 (1):1–10. doi:10.1186/1029-242X-2012-50.
   Web of Science ®Google Scholar
• Wu, Q. Y. 2020. Precise asymptotics for complete integral convergence under sublinear expectations. Mathematical Problems in Engineering 2020 (1):1–13. doi:10.1155/2020/3145935.
   Web of Science ®Google Scholar
• Wu, P. Y., and Z. J. Chen. 2015. Invariance principles for the law of the iterated logarithm under G-framework. Science China Mathematics 58 (6):1251–64. doi:10.1007/s11425-015-5002-8.
   Web of Science ®Google Scholar
• Wu, Q. Y., and Y. Y. Jiang. 2018. Strong law of large numbers and Chover’s law of the iterated logarithm under sub-linear expectations. Journal of Mathematical Analysis and Applications 460 (1):252–70. doi:10.1016/j.jmaa.2017.11.053.
   Web of Science ®Google Scholar
• 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 87 (3):409–23. doi:10.1080/17442508.2014.959951.
   Google Scholar
• Yao, C., Y. P. He, R. Wang, and X. J. Wang. 2020. Laws of large numbers and complete convergence for WOD random variables and their applications. Communications in Statistics - Simulation and Computation :1–26. doi:10.1080/03610918.2020.1851714.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Zhang, L. X. 2021. Heyde’s theorem under the sub-linear expectations. Statistics & Probability Letters 170:108987. doi:10.1016/j.spl.2020.108987.
   Web of Science ®Google Scholar