| Mathematics and Computer Science |
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| 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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Abstract Let {Yi, -∞ < i < ∞} be a sequence of identically distributed NSD random variables, and {ai, -∞ < 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.
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Received: 09 December 2018
Published: 25 March 2020
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Cite this article:
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.
URL:
https://www.zjujournals.com/sci/EN/Y2020/V47/I2/172
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NSD序列生成的移动平均过程的矩完全收敛性
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
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