| 强平稳\rho-混合序列的精确渐近性 |
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| 引用本文： | 赵月旭.强平稳\rho-混合序列的精确渐近性[J].系统科学与数学,2008,28(7):822-832. |
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| 作者姓名： | 赵月旭 |
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| 作者单位： | (1)浙江大学数学系, 杭州 310027; 杭州电子科技大学应用数学与工程计算研究所, 杭州310018; (2)上海交通大学数学系, 上海 200030; (3)杭州电子科技大学应用数学与工程计算研究所, 杭州 310018. |
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| 摘 要： | 研究了强平稳\rho-混合序列部分和S_{n}=X_{1}+X_{2}+...+X_{n}的精确渐近性:即当\varepsilon\searrow 0时,概率级数\sum\limits_{n=1}^{\infty}\varphi(n)P(|S_{n}|\geq \varepsilon H(n))的极限行为和收敛速度,并揭示了函数\varphi(n)$与$H(n)之间的关系.
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| 关 键 词： | \rho-混合 部分和 混合速度 精确渐近性. |
| 收稿时间： | 2006-6-1 |
| 修稿时间： | 2007-5-11 |
Precise Asymptotics of Strictly Stationary \rho-Mixing Sequences |
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| ZHAO Yuexu,MA Zhihao,SUN Weiliang.Precise Asymptotics of Strictly Stationary \rho-Mixing Sequences[J].Journal of Systems Science and Mathematical Sciences,2008,28(7):822-832. |
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| Authors: | ZHAO Yuexu MA Zhihao SUN Weiliang |
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| Institution: | (1)Department of Mathematics, Zhejiang University, Hangzhou 310027; Institute of Applied Mathematics and Engineering Computation, Hangzhou Dianzi University, Hangzhou 310018; (2)Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030; (3)Institute of Applied Mathematics and Engineering Computation, Hangzhou Dianzi University, Hangzhou 310018. |
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| Abstract: | The precise asymptotics for partial sums S_{n}=X_{1}+X_{2}+\cdots+X_{n}of strictly stationary \rho-mixing sequences are investigated, and the limit properties and the convergence rate of series \sum\limits_{n=1}^{\infty}\varphi(n)P(|S_{n}|\geq \varepsilon H(n)) as \varepsilon\searrow 0 are given, and hence the relations between functions \varphi(n) and H(n) are revealed. |
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| Keywords: | \rho-mixing partial sums mixing rate precise asymptotics |
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