华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (3): 56-60,96.

• 应用数学与基础数学 • 上一篇    下一篇

无穷小非交换概率空间中的极限定理

崔汉哲1,2, 薛以锋1   

  1. 1. 华东师范大学~~数学系, 上海 200241; 2. 上海电机学院~~数理教学部, 上海 200240
  • 收稿日期:2011-07-01 修回日期:2011-10-01 出版日期:2012-05-25 发布日期:2012-05-22

Limit theorems in infinitesimal non-commutative probability spaces

CUI Han-zhe 1,2, XUE Yi-feng 1   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200241, China; 2. Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 200240, China
  • Received:2011-07-01 Revised:2011-10-01 Online:2012-05-25 Published:2012-05-22

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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.}

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

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.

Key words: infinitesimal non-commutative probability spaces, central limit theorems, Poisson limit theorem

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