Precise Asymptotics of Strictly Stationary \rho-Mixing Sequences

ZHAO Yuexu; MA Zhihao; SUN Weiliang

doi:10.12341/jssms10204

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Journal of Systems Science and Mathematical Sciences ›› 2008, Vol. 28 ›› Issue (7) : 822-832. DOI: 10.12341/jssms10204

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

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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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Received	Revised	Published
2006-06-01	2007-05-11	2008-07-25
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2008-07-25

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