次线性期望空间下广义负相依序列加权和的完全收敛性

doi:10.3969/j.issn.1000-5641.2023.02.004

华东师范大学学报（自然科学版） ›› 2023, Vol. 2023 ›› Issue (2): 17-25.doi: 10.3969/j.issn.1000-5641.2023.02.004

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

信阳学院数学与统计学院, 河南信阳　464000

收稿日期:2021-04-19 出版日期:2023-03-25 发布日期:2023-03-23
作者简介:费丹丹, 女, 讲师, 研究方向为概率极限理论. E-mail: fdd_together@163.com
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)

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

Dandan FEI(), Zongkui FU

School of Mathematics and Statistics, Xinyang College, Xinyang, Henan　464000, China

Received:2021-04-19 Online:2023-03-25 Published:2023-03-23

摘要/Abstract

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

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

中图分类号:

O211.4

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.

Dandan FEI, Zongkui FU. Complete convergence of weighted sums for extended negatively dependent sequences under sublinear expectation[J]. Journal of East China Normal University(Natural Science), 2023, 2023(2): 17-25.

参考文献 11

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次线性期望空间下广义负相依序列加权和的完全收敛性

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

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