| 关于独立同分布随机序列的若干极限定理 |
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| 引用本文： | 简旭,吴玉,范爱华.关于独立同分布随机序列的若干极限定理[J].安徽工业大学学报,2014(2):209-211. |
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| 作者姓名： | 简旭 吴玉 范爱华 |
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| 作者单位： | 安徽工业大学数理学院,安徽马鞍山243032 |
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| 基金项目： | 安徽省自然科学基金（1408085MA04）;安徽工业大学研究生创新基金资助（201289） |
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| 摘 要： | 利用Borel-Cantelli引理与概率论极限理论中的纯分析方法,给出了独立同分布随机序列滑动平均的熵定理和中心极限定理。概率论中关于独立同分布的经典结果—渐近均分性定理以及中心极限定理是本文的推论。
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| 关 键 词： | 熵 Borel-Cantelli引理 强极限定理 中心极限定理 |
On Some Limit Theorems for Identically Independent Distributed Random Sequence |
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| JIAN Xu,WU Yu,FAN Aihua.On Some Limit Theorems for Identically Independent Distributed Random Sequence[J].Journal of Anhui University of Technology,2014(2):209-211. |
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| Authors: | JIAN Xu WU Yu FAN Aihua |
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| Affiliation: | (School of Mathematics and Physics, Anhui University of Technology, Ma＇anshan 243032, China) |
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| Abstract: | By using Borel Cantelli lernma and the pure analysis method of probability limit theory, the moving average entropy theorem and the central limit theorem for independent identically distributed random sequence are obtained, which generalizes some classical results and makes the classical theorem of asymptotic equipartition theorem and the central limit theorem of independent identically distributed random variables as the corollaries of this paper. |
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| Keywords: | entropy Borel-Cantelli lemma strong limit theorem central limit theorem |
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