Complete convergence theorems for moving average process generated by independent random variables under sub-linear expectations

References

• Chen, P. Y., and S. H. Sung. 2021. Complete convergence for weighted sums of widely orthant-dependent random variables. Journal of Inequalities and Applications 2021 (1):1–16. doi: 10.1186/s13660-021-02574-2.
   Web of Science ®Google Scholar
• Chen, X., and Q. Wu. 2022. Complete convergence and complete integral convergence of partial sums for moving average process under sub-linear expectations. AIMS Mathematics 7 (6):9694–715. 10.3934/math.2022540. doi: 10.3934/math.2022540.
   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
• Deng, X., and X. J. Wang. 2020. On complete convergence for extended independent random variables under sub-linear expectations. Journal of the Korean Mathematical Society 2020 (57):553–70. doi: 10.4134/JKMS.j190093.
   Web of Science ®Google Scholar
• Guan, L. H., Y. S. Xiao, and Y. N. Zhao. 2021. Complete moment convergence of moving average processes for m-WOD sequence. Journal of Inequalities and Applications 2021 (16):1–12. doi: 10.1186/s13660-021-02546-6.
   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.33.2.25.16578237
   PubMed Web of Science ®Google Scholar
• Ibragimov, I. A. 1962. Some limit theorems for stationary processes. Theory of Probability & Its Applications 7 (4):349–82. doi: 10.1137/1107036.
   Google Scholar
• Li, D., M. Bhaskara Rao, and X. Wang. 1992. Complete convergence of moving average processes. Statistics & Probability Letters 14 (2):111–4. doi: 10.1016/0167-7152(92)90073-E.
   Web of Science ®Google Scholar
• Peng, S. 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
• Peng, S. G. 2006. G-expectation, G-Brownian motion and related stochastic calculus of Itô type. Stochastic Analysis and Applications 2 (4):541–67.
   Google Scholar
• Peng, S. 2009. Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations. Science in China Series A: Mathematics 52 (7): 1391–411. doi: 10.1007/s11425-009-0121-8.
   Google Scholar
• Shen, A., M. Xue, and W. 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.
   Web of Science ®Google Scholar
• Song, M. Z., and Q. X. Zhu. 2020. Complete moment convergence of extended negatively dependent random variables. Journal of Inequalities and Applications 2020 (150):1–13. doi: 10.1186/s13660-020-02416-7.
   Web of Science ®Google Scholar
• Tao, X., Y. Wu, H. Xia, and X. Wang. 2017. Complete convergence of moving average process based on widely orthant dependent random variables. Revista De La Real Academia De Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 111 (3):809–21. doi: 10.1007/s13398-016-0323-1.
   Web of Science ®Google Scholar
• Wang, X. J., and S. H. Hu. 2014. Complete convergence and complete moment convergence for martingale difference sequence. Acta Mathematica Sinica, English Series 30 (1):119–32. doi: 10.1007/s10114-013-2243-8.
   Web of Science ®Google Scholar
• Wu, Q. 2021. Complete convergence for END random variables under sublinear expectations. Discrete Dynamics in Nature and Society 2021:1–10. doi: 10.1155/2021/5529109.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Wu, Q., and 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., M. Zhai, and J. Peng. 2019. On the complete convergence for weighted sums of extended negatively dependent random variables. Journal of Mathematical Inequalities 13 (1):251–60. doi: 10.7153/jmi-2019-13-18.
   Web of Science ®Google Scholar
• Xu, J. P., and L. X. Zhang. 2019. Three series theorem for independent random variables under sub-linear expectations with applications. Acta Mathematica Sinica, English Series 35 (2):172–84. doi: 10.1007/s10114-018-7508-9.
   Web of Science ®Google Scholar
• Xu, M. Z., and K. Cheng. 2021. Convergence for sums of i.i.d.random variables under sublinear expectations. Journal of Inequalities and Applications 2021 (157):1–14. doi: 10.1186/s13660-021-02692-x.
   Web of Science ®Google Scholar
• Zhang, L.-X. 1996. Complete convergence of moving average processes under dependence assumptions. Statistics & Probability Letters 30 (2):165–70. doi: 10.1016/0167-7152(95)00215-4.
   Web of Science ®Google Scholar
• Zhang, L. 2016. 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
• Zhang, L. 2016. Exponential inequalities under the 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. 2022. Strong limit theorems for extended independent random variables and extended negatively dependent random variables under sub-linear expectations. Acta Mathematica Scientia 42 (2):467–90. doi: 10.1007/s10473-022-0203-z.
   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):1–14. doi: 10.1186/s13660-017-1538-1.
   PubMed Web of Science ®Google Scholar