| 无穷小非交换概率空间中的极限定理 |
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| 引用本文： | 崔汉哲,薛以锋.无穷小非交换概率空间中的极限定理[J].华东师范大学学报(自然科学版),2012,2012(3):56-60,96. |
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| 作者姓名： | 崔汉哲 薛以锋 |
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| 作者单位： | 1. 华东师范大学数学系,上海200241;上海电机学院数理教学部,上海200240
2. 华东师范大学数学系,上海,200241 |
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| 摘 要： | 在无穷小非交换概率空间中, 利用\,$R$\,变换证明了一维和多维情形下的中心极限定理, 利用矩函数和累积函数的关系证明了泊松极限定理, 并通过组合分析的方法给出了标准半单位圆元素与自由泊松元素之间的关系.}
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| 关 键 词： | 无穷小非交换概率空间 中心极限定理 泊松极限定理 |
| 收稿时间： | 2011-07-01 |
Limit theorems in infinitesimal non-commutative probability spaces |
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| CUI Han-zhe
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XUE Yi-feng.Limit theorems in infinitesimal non-commutative probability spaces[J].Journal of East China Normal University(Natural Science),2012,2012(3):56-60,96. |
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| Authors: | CUI Han-zhe XUE Yi-feng |
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| Institution: | 1 (1.Department of Mathematics,East China Normal University,Shanghai 200241,China; 2.Department of Mathematics and Physics,Shanghai Dianji University, Shanghai 200240,China) |
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| Abstract: | This paper proved the central limit theorems in infinitesimal non-commutative probability spaces using R transform under both one-dimension and multi-dimension cases. Also Poisson limit theorem was proved using the moments-cumulants formula.Lastly,the relation between the standard semicircular elements and free poisson elements was figured out by combinatorial analysis. |
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| Keywords: | infinitesimal non-commutative probability spaces central limit theorems Poisson limit theorem |
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