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Xu, Mingzhou; Kong, Xuhang

Complete \(q\)th moment convergence of moving average processes for \(m\)-widely acceptable random variables under sub-linear expectations. (English) Zbl 07913932

Stat. Probab. Lett. 214, Article ID 110203, 8 p. (2024).
Summary: In this article, we studied complete \(q\)th moment convergence of the moving average processes produced by \(m\)-widely acceptable (\(m\)-WA) random variables under sub-linear expectations. The results here extend those of the moving average processes generated by \(m\)-WOD random variables in probability.

MSC:

60F15 Strong limit theorems
60F05 Central limit and other weak theorems

Keywords:

moving average processes; \(m\)-widely acceptable random variables; complete \(q\)-moment convergence; sub-linear expectations
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References:

[1] Chen, Z., Strong laws of large numbers for sub-linear expectations, Sci. China Math., 59, 5, 945-954, 2016 · Zbl 1341.60015
[2] Gao, F.; Xu, M., Large deviations and moderate deviations for independent random variables under sublinear expectations, Sci. China Math. (in Chinese), 41, 4, 337-352, 2011 · Zbl 1488.60043
[3] Hosseini, S. M.; Nezakati, A., Complete moment convergence for the dependent linear processes with random coefficients, Acta Math. Sin. (Engl. Ser.), 35, 8, 1321-1333, 2019 · Zbl 1420.60041
[4] Hu, F.; Chen, Z.; Zhang, D., How big are the increments of G-Brownian motion?, Sci. China Math., 57, 8, 1687-1700, 2014 · Zbl 1301.60068
[5] Hu, Z.-C.; Yang, Y.-Z., Some inequalities and limit theorems under sublinear expectations, Acta Math. Appl. Sin. Engl. Ser., 33, 2, 451-462, 2017 · Zbl 1370.60054
[6] Ko, M.-H., Complete moment convergence of moving average process generated by a class of random variables, J. Inequal. Appl., 2015, 1, 1-9, 2015 · Zbl 1335.60039
[7] Kuczmaszewska, A., Complete convergence for widely acceptable random variables under the sublinear expectations, J. Math. Anal. Appl., 484, 1, Article 123662 pp., 2020 · Zbl 1471.60041
[8] Meng, B.; Wang, D.; Wu, Q., Convergence of asymptotically almost negatively associated random variables with random coefficients, Comm. Statist. Theory Methods, 1-15, 2021
[9] Peng, S., G-expectation, G-Brownian motion and related stochastic calculus of Itô type, (Stochastic Analysis and Applications, vol. 2, 2007, Springer: Springer USA), 541-567 · Zbl 1131.60057
[10] Peng, S., Nonlinear Expectations and Stochastic Calculus Under Uncertainty: with Robust CLT and G-Brownian Motion, 2019, Springer Nature: Springer Nature Berlin, Germany · Zbl 1427.60004
[11] Song, M.; Wu, Y.; Chu, Y., Complete \(q\) th-moment convergence of moving average process for \(m\)-WOD random variable, Wuhan Univ. J. Nat. Sci., 27, 5, 396-404, 2022
[12] Wu, Q.; Jiang, Y., Strong law of large numbers and Chover’s law of the iterated logarithm under sub-linear expectations, J. Math. Anal. Appl., 460, 1, 252-270, 2018 · Zbl 1380.60039
[13] Xu, M., Complete convergence of moving average processes produced by negatively dependent random variables under sub-linear expectations, AIMS Math., 8, 7, 17067-17080, 2023
[14] Xu, M., On the complete moment convergence of moving average processes generated by negatively dependent random variables under sub-linear expectations, AIMS Math., 9, 2, 3369-3385, 2024
[15] Xu, M.; Cheng, K., Convergence for sums of iid random variables under sublinear expectations, J. Inequal. Appl., 2021, 1, 1-14, 2021 · Zbl 1504.60052
[16] Xu, M.; Cheng, K., How small are the increments of G-Brownian motion, Statist. Probab. Lett., 186, 1-9, 2022 · Zbl 1492.60144
[17] Xu, M.; Cheng, K.; Yu, W., Complete convergence and complete integral convergence of partial sums for moving average process under sub-linear expectations, AIMS Math., 7, 11, 19998-20019, 2022
[18] Xu, M.; Cheng, K.; Yu, W., Convergence of linear processes generated by negatively dependent random variables under sub-linear expectations, J. Inequal. Appl., 2023, 2023 · Zbl 1532.60062
[19] Xu, M.; Kong, X., Note on complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations, AIMS Math., 8, 4, 8504-8521, 2023
[20] Xu, M.; Kong, X., Complete moment convergence of moving average processes for \(m\)-widely acceptable sequence under sub-linear expectations, 2024, arXiv preprint arXiv:2403.18304v1
[21] Zhang, L.-X., Donsker’s invariance principle under the sub-linear expectation with an application to Chung’s law of the iterated logarithm, Commun. Math. Stat., 3, 2, 187-214, 2015 · Zbl 1321.60067
[22] Zhang, L., Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm, Sci. China Math., 59, 12, 2503-2526, 2016 · Zbl 1362.60031
[23] Zhang, L., Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications, Sci. China Math., 59, 4, 751-768, 2016 · Zbl 1338.60095
[24] Zhang, L., On the laws of the iterated logarithm under sub-linear expectations, Probab., Uncertain. Quant. Risk, 6, 4, 409-460, 2021 · Zbl 1491.60047
[25] Zhang, L.-X., Strong limit theorems for extended independent random variables and extended negatively dependent random variables under sub-linear expectations, Acta Math. Sci., 42, 2, 467-490, 2022 · Zbl 1513.60037
[26] Zhang, Y.; Ding, X., Further research on complete moment convergence for moving average process of a class of random variables, J. Inequal. Appl., 2017, 1, 1-11, 2017 · Zbl 1395.60037
[27] Zhang, L.; Lin, J., Marcinkiewicz’s strong law of large numbers for nonlinear expectations, Statist. Probab. Lett., 137, 269-276, 2018 · Zbl 1406.60049
[28] Zhong, H.; Wu, Q., Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation, J. Inequal. Appl., 2017, 1, 1-14, 2017 · Zbl 1386.60117
[29] Zhou, X., Complete moment convergence of moving average processes under \(\varphi \)-mixing assumptions, Statist. Probab. Lett., 80, 5-6, 285-292, 2010 · Zbl 1186.60031
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