Journal of Jilin University Science Edition
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GUAN Lihong, LI Yinghong
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Abstract: Let {Sk, k≥1} be a random sequence satisfying the almost sure central limit theorem, and {Tk, k≥1} be a random sequence with Tk→0(or 1) a.s. By using the limit theory, we proved that {Sk+Tk, k≥1} and {Sk/Tk, k≥1} satisfied the almost sure central limit theorem, and gave some examples such as linear processes, selfnormalized sums, error variance estimates in linear models and products of partial sums.
Key words: selfnormalized sum, linear processes, product of partial sum, almost sure central limit theorem
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GUAN Lihong, LI Yinghong. A Note on Almost Sure Central Limit Theorems for Random Sequences[J].Journal of Jilin University Science Edition, 2018, 56(2): 306-310.
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http://xuebao.jlu.edu.cn/lxb/EN/Y2018/V56/I2/306
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