| 在${\mathbb{R}}^m$中重对数广义律的精确速率 |
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| 引用本文： | 徐明周,丁云正,周永正.在${\mathbb{R}}^m$中重对数广义律的精确速率[J].数学研究及应用,2018,38(1):103-110. |
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| 作者姓名： | 徐明周 丁云正 周永正 |
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| 作者单位： | 景德镇陶瓷大学信息工程学院, 江西 景德镇 333403,景德镇陶瓷大学信息工程学院, 江西 景德镇 333403,景德镇陶瓷大学信息工程学院, 江西 景德镇 333403 |
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| 基金项目： | 国家自然科学基金(Grant No.61662037), 江西省教育厅科学技术项目(Grant Nos.GJJ150894; GJJ150905). |
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| 摘 要： | 令\{$X$, $X_n$, $n\ge 1$\}是期望为${\mathbb{E}}X=(0,\ldots,0)_{m\times 1}$和协方差阵为${\rm Cov}(X,X)=\sigma^2I_m$的独立同分布的随机向量列, 记$S_n=\sum_{i=1}^{n}X_i$, $n\ge 1$. 对任意$d>0$和$a_n=o((\log\log n)^{-d})$, 本文研究了${{\mathbb{P}}(|S_n|\ge (\varepsilon+a_n)\sigma \sqrt{n}(\log\log n)^d)$的一类加权无穷级数的重对数广义律的精确速率.
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| 关 键 词： | 精确速率 重对数律 完全收敛 独立同分布的随机向量 |
| 收稿时间： | 2017/2/6 0:00:00 |
| 修稿时间： | 2017/8/4 0:00:00 |
Precise Rates in the Generalized Law of the Iterated Logarithm in ${\mathbb{R}}^m$ |
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| Mingzhou XU,Yunzheng DING and Yongzheng ZHOU.Precise Rates in the Generalized Law of the Iterated Logarithm in ${\mathbb{R}}^m$[J].Journal of Mathematical Research with Applications,2018,38(1):103-110. |
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| Authors: | Mingzhou XU Yunzheng DING and Yongzheng ZHOU |
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| Institution: | School of Information and Engineering, Jingdezhen Ceramic University, Jiangxi 333403, P. R. China,School of Information and Engineering, Jingdezhen Ceramic University, Jiangxi 333403, P. R. China and School of Information and Engineering, Jingdezhen Ceramic University, Jiangxi 333403, P. R. China |
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| Abstract: | Let \{$X$, $X_n$, $n\ge 1$\} be a sequence of i.i.d. random vectors with ${\mathbb{E}}X=(0,\ldots,0)_{m\times 1}$ and ${\rm Cov}(X,X)=\sigma^2I_m$, and set $S_n=\sum_{i=1}^{n}X_i$, $n\ge 1$. For every $d>0$ and $a_n=o((\log\log n)^{-d})$, the article deals with the precise rates in the genenralized law of the iterated logarithm for a kind of weighted infinite series of ${\mathbb{P}}(|S_n|\ge (\varepsilon+a_n)\sigma \sqrt{n}(\log\log n)^d)$. |
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| Keywords: | precise rates law of iterated logarithm complete convergence i i d random vectors |
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