| 强混合序列部分和乘积的渐近正态性 |
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| 引用本文： | 刘君,王辛刚,张冬梅. 强混合序列部分和乘积的渐近正态性[J]. 吉林大学学报(理学版), 2009, 47(6): 1196-1198 |
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| 作者姓名： | 刘君 王辛刚 张冬梅 |
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| 作者单位： | 北华大学,数学学院,吉林,吉林,132013;浙江工业大学,信息工程学院,杭州,310032;浙江工业大学,理学院,杭州,310032 |
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| 摘 要： | 设{Xn,n≥1}是同分布正的强混合随机变量序列. 利用强混合序列的中心极限定理以及大数定律, 在适当的条件下证明了 N为标准正态随机变量.
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| 关 键 词： | 强混合序列 部分和乘积 中心极限定理 同分布 对数正态 |
| 收稿时间： | 2009-03-10 |
Asymptotic Distribution of the Product of Strong Mixing Sums |
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| LIU Jun,WANG Xin-gang,ZHANG Dong-mei. Asymptotic Distribution of the Product of Strong Mixing Sums[J]. Journal of Jilin University: Sci Ed, 2009, 47(6): 1196-1198 |
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| Authors: | LIU Jun WANG Xin-gang ZHANG Dong-mei |
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| Affiliation: | 1. College of Mathematics, Beihua University, Jilin 132013, Jilin Province, China;2. College of Information Engineering, Zhejiang University of Technology, Hangzhou 310032, China;3. College of Science, Zhejiang University of Technology, Hangzhou 310032, China |
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| Abstract: | Let { X_n, n≥1} be a sequence of strong mixing identically distributed positive random variable, under some suitable conditions, by means of the central limit theorem and the law of large numbers of strong mixing sequence, it is proved that (∏_(k_1)~nS_k/n!μ~n)~(1/(γσ_n))d→ e~N, n →∞ , where S_k = ∑_(I=1)~k X_I,μ= EX_1 > 0, σ~2 = Var X_1 < ∞, γ =σ/μ,σ_n~2 = Var(1/γ ∑_(k=1)~n (S_k/kμ - 1 )), and N is a standrad normal random variable. |
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| Keywords: | strong mixing sequences product of sums central limit theorem identically distribution lognormal distribution |
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