Cumulants in noncommutative probability theory I. Noncommutative exchangeability systems
Cumulants in noncommutative probability theory I. Noncommutative exchangeability systems
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DOI：
10.1007/s00209-004-0653-0
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发表时间：
2002-10
影响因子：
0.8
通讯作者：
F. Lehner
中科院分区：
文献类型：
--
作者：
F. Lehner
累积量使测量的卷积线性化。我们使用 Good 公式在非常一般的环境中定义非交换累积量。事实证明，所需的基本属性是随机变量的可交换性。粗略地说，该公式表示累积量是随机变量的某个“离散傅里叶变换”的矩。这提供了一种简单的统一方法来理解累积量的已知示例，例如经典累积量、自由累积量和各种 q 累积量。
Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting. It turns out that the essential property needed is exchangeability of random variables. Roughly speaking the formula says that cumulants are moments of a certain ‘‘discrete Fourier transform’’ of a random variable. This provides a simple unified method to understand the known examples of cumulants, like classical, free and variousq-cumulants.