| NA序列部分和之和乘积的极限定理 |
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| 引用本文： | 李雪峰,陆冬梅.NA序列部分和之和乘积的极限定理[J].吉林大学学报(理学版),2022,60(4):873-880. |
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| 作者姓名： | 李雪峰 陆冬梅 |
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| 作者单位： | 长春电子科技学院, 长春 130114 |
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| 摘 要： | 设{Xn, n≥1}是一严平稳正值负相关(NA)随机变量序列, 满足EX1=μ>0, Var X1=σ2<∞. 首先利用NA序列加权和的中心强极限定理和矩不等式证明, 其中N为标准正态随机变量; 其次, 对于边界函数和拟权函数给出NA序列部分和之和乘积的完全收敛性中精确渐近性的一般结果.
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| 关 键 词： | NA序列 部分和之和乘积 渐近分布 精确渐近性 |
| 收稿时间： | 2021-10-10 |
Limit Theorems of Products of Sums of Partial Sums of NA Sequence |
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| LI Xuefeng,LU Dongmei.Limit Theorems of Products of Sums of Partial Sums of NA Sequence[J].Journal of Jilin University: Sci Ed,2022,60(4):873-880. |
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| Authors: | LI Xuefeng LU Dongmei |
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| Institution: | Chuangchun College of Electronic Technology, Changchun 130114, China |
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| Abstract: | Let {Xnn, n≥1} be a strictly stationary negatively associated (NA) sequence of positive random variables with EX1=μ>0, and
Var X1=σ2<∞. Firstly, by using the central strong limit theorems and moment inequalities of weighted sums of NA sequence,
where N is a standard normal random variable. Secondly, we give a general result of precise asymptotics in complete convergence for products of sums of partial sums of NA sequence for the boundary function and quasi weight function. |
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| Keywords: | NA sequence product of sums of partial sums asymptotic distribution precise asymptotics |
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