强平稳\rho-混合序列的精确渐近性

赵月旭;麻志浩;孙伟良

系统科学与数学 ›› 2008, Vol. 28 ›› Issue (7) : 822-832.

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系统科学与数学 ›› 2008, Vol. 28 ›› Issue (7) : 822-832. DOI: 10.12341/jssms10204
论文

强平稳\rho-混合序列的精确渐近性

    赵月旭(1); 麻志浩(2); 孙伟良(3)
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Precise Asymptotics of Strictly Stationary \rho-Mixing Sequences

    ZHAO Yuexu(1), MA Zhihao(2), SUN Weiliang(3)
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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.

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.

关键词

\rho-混合 / 部分和 / 混合速度 / 精确渐近性.

Key words

\rho-mixing / partial sums / mixing rate / precise asymptotics.

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赵月旭 , 麻志浩 , 孙伟良. 强平稳\rho-混合序列的精确渐近性. 系统科学与数学, 2008, 28(7): 822-832. https://doi.org/10.12341/jssms10204
ZHAO Yuexu , MA Zhihao , SUN Weiliang. Precise Asymptotics of Strictly Stationary \rho-Mixing Sequences. Journal of Systems Science and Mathematical Sciences, 2008, 28(7): 822-832 https://doi.org/10.12341/jssms10204
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