华东师范大学学报（自然科学版） >

2023 , Vol. 2023 >Issue 2: 17 - 25

DOI: https://doi.org/10.3969/j.issn.1000-5641.2023.02.004

数学

次线性期望空间下广义负相依序列加权和的完全收敛性

  • 费丹丹 ,
  • 付宗魁
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  • 信阳学院 数学与统计学院, 河南 信阳　464000
费丹丹, 女, 讲师, 研究方向为概率极限理论. E-mail: fdd_together@163.com

收稿日期: 2021-04-19

  网络出版日期: 2023-03-23

基金资助

河南省高等学校重点科研项目 (21B110006); 河南省高等学校青年骨干教师培养计划 (2018GGJS198); 信阳学院校级一般项目 (2019-XJLYB-003, 2020-XJLYB-003)

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Complete convergence of weighted sums for extended negatively dependent sequences under sublinear expectation

  • Dandan FEI ,
  • Zongkui FU
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  • School of Mathematics and Statistics, Xinyang College, Xinyang, Henan　464000, China

Received date: 2021-04-19

  Online published: 2023-03-23

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摘要

研究了次线性期望空间下随机变量序列的完全收敛性, 利用广义负相依序列的性质, 在随机变量的 $ \lambda $ 阶上积分存在的条件下, 得到了次线性期望空间下广义负相依序列加权和的完全收敛性, 推广和改进了经典概率空间中独立序列的结果.

关键词： 次线性期望空间; 广义负相依序列; 完全收敛性

本文引用格式

费丹丹 , 付宗魁 . 次线性期望空间下广义负相依序列加权和的完全收敛性[J]. 华东师范大学学报（自然科学版）, 2023 , 2023(2) : 17 -25 . DOI: 10.3969/j.issn.1000-5641.2023.02.004

Abstract

The complete convergence of sequences of random variables under sublinear expectation was studied. Using the properties of extended negatively dependent (ND) sequences, under the condition that the $ \lambda $ -order Choquet integrals of the random variable are finite, the complete convergence of the weighted sums for extended ND sequences under a sublinear expectation was proved. The results generalize and improve the results of independent sequences in the classical probability space.

Key words： sublinear expectation; extended negatively dependent sequence; complete convergence

参考文献

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