Complete convergence of weighted sums for extended ND random variables sequence under sub-linear expectation

doi:10.3969/j.issn.0253-2778.2018.08.006

Journal of University of Science and Technology of China ›› 2018, Vol. 48 ›› Issue (8): 637-642.DOI: 10.3969/j.issn.0253-2778.2018.08.006

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Complete convergence of weighted sums for extended ND random variables sequence under sub-linear expectation

LIANG Haiye,WU Qunying

College of Science,Guilin University of Technology, Guilin 541004, China

Received:2018-03-23 Revised:2018-04-17 Accepted:2018-04-17 Online:2018-08-31 Published:2018-04-17

Abstract

Abstract: The complete convergence of weighted sums for extended ND under sub-linear expectation was studied. With the condition of the p order Choquet integrals of the random variable being finite, the complete convergence of weighted sums for extended ND random variables sequence in the probability space was extended to the sub-linear expectations space.

Key words: sub-linear expectation, complete convergence, weighted sum, extended ND random variables sequence

CLC Number:

O211.4

LIANG Haiye,WU Qunying. Complete convergence of weighted sums for extended ND random variables sequence under sub-linear expectation[J]. Journal of University of Science and Technology of China, 2018, 48(8): 637-642.

References

［1］
PENG S. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation[J]. Stochastic Process, 2008, 118(12): 2223-2253.
[2] PENG S. A new central limit theorem under sub-linear expectations[EB/OL]. [2018-03-01] https://arxiv.org/abs/0803.2656.

[3] ZHANG L X. Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations[EB/OL]. [2018-03-01] https://arxiv.org/abs/ 1608.00710.

[4] ZHANG L X. Exponential inequalities under sub-linear expectations with applications to laws of the iterated logarithm[J]. Science China, 2014, 59(12):2503-2526.
[5] ZHANG L X. Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications[J]. Science China, 2016, 59(4):751-768.
[6] WU Q, JIANG Y. Strong law of large numbers and Chover’s law of the iterated logarithm under sub-linear expectations[J]. Journal of Mathematical Analysis & Applications, 2018, 460(1): 252-270.
[7] HU C, DATTA S, KOUL H L. A strong law of large numbers for sub-linear expectation under a general moment condition[J]. Statistics & Probability Letters, 2016, 119: 248-258.
[8] WU Q. Complete convergence for negatively dependent sequences of random variables[J]. Journal of Inequalities & Applications, 2010, 2010(1):1-10.
[9] WU Q. A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables[J]. Journal of Inequalities & Applications, 2012, 2012(1): 1-10.
[10] 孟兵, 吴群英. ND阵列加权乘积和的完全收敛性[J]. 纯粹数学与应用数学, 2010, 26(1):84-90.
MENG Bing, WU Qunying. Complete convergence for weighted sums of arrays of ND random variables[J]. Pure and Applied Mathematics, 2010, 26(1):84-90.
[11] 甘师信, 陈平炎. NOD序列加权和的强收敛速度[J]. 数学物理学报, 2008, 28(2):283-290.
GAN Shixin, CHEN Pingyan. Strong convergence rate of weighted sums for NOD sequences[J]. Acta Mathematica Scientia, 2008, 28(2):283-290.
[12] ZHONG H, WU Q. Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation[J]. Journal of Inequalities & Applications, 2017, 2017(1): 261.

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[1]	LI Xiang, SHEN Aiting. Complete moment convergence for weighted sums of extended negatively dependent random variables [J]. Journal of University of Science and Technology of China, 2020, 50(2): 156-162.
[2]	YU Donglin, WU Qunying. Marcinkiewicz type complete convergence for weighted sums under sub-linear expectations [J]. Journal of University of Science and Technology of China, 2018, 48(2): 89-96.
[3]	ZHENG Lulu, WANG Qiang, WANG Xuejun. Strong convergence for weighted sums of negatively superadditive dependent random variables [J]. Journal of University of Science and Technology of China, 2015, 45(2): 101-106.

Complete convergence of weighted sums for extended ND random variables sequence under sub-linear expectation

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