NSD序列生成的移动平均过程的矩完全收敛性

doi:10.3785/j.issn.1008-9497.2020.02.007

浙江大学学报（理学版）

2020, Vol. 47

Issue (2): 172-177 DOI: 10.3785/j.issn.1008-9497.2020.02.007

数学与计算机科学

NSD序列生成的移动平均过程的矩完全收敛性

高云峰¹, 邹广玉²

1.吉林农业科技学院电气与信息工程学院，吉林吉林 132101
2.长春工程学院理学院，吉林长春 130012

Complete moment convergence for moving average processes generated by NSD sequences

GAO Yunfeng¹, ZOU Guangyu²

1.College of Electrical and Information Engineering, Jilin Agriculture Science and Technology College, Jilin 132101,Jilin Province， China
2.School of Science, Changchun Institute of Technology, Changchun 130012, China

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摘要： 设$\{Y_{i},-∞ < i < ∞\}$为一同分布的NSD随机变量序列，$\{a_{i},-∞ < i < ∞\}$为一绝对可和的实数序列。利用NSD序列的矩不等式以及缓变函数的性质，在适当的条件下，得到了由NSD序列生成的移动平均过程的矩完全收敛性和强大数定律，改进和推广了已有的结果。

关键词： 矩完全收敛性; NSD序列; 强大数定律

Abstract: Let {Y_i, -∞ < i < ∞} be a sequence of identically distributed NSD random variables, and {a_i, -∞ < i < ∞} be an absolutely summable sequence of real numbers. By using the moment inequality of NSD sequence and the property of slowly varying function, we obtain the complete moment convergence and strong law of large numbers for moving average processes generated by NSD sequences under some suitable conditions, which promote and improve the corresponding results.

Key words: moving average process complete moment convergence NSD sequence strong law of large numbers

收稿日期: 2018-12-09 出版日期: 2020-03-25

CLC:

O211.4

基金资助: 国家自然科学基金资助项目(11401090).

作者简介: 高云峰(1973—)，ORCID:http://orcid.org/0000-0002-3951-7037，男，硕士，副教授，主要从事概率论与数理统计研究，E-mail:203063186@qq.com.

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引用本文:

高云峰, 邹广玉. NSD序列生成的移动平均过程的矩完全收敛性[J]. 浙江大学学报（理学版）, 2020, 47(2): 172-177.

GAO Yunfeng, ZOU Guangyu. Complete moment convergence for moving average processes generated by NSD sequences. Journal of Zhejiang University (Science Edition), 2020, 47(2): 172-177.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.02.007 或 https://www.zjujournals.com/sci/CN/Y2020/V47/I2/172

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