Cumulants in noncommutative probability theory I. Noncommutative exchangeability systems

被引：0
作者：
Franz Lehner
机构：
[1] Technische Universität Graz,Institut für Mathematik C
来源：
Mathematische Zeitschrift | 2004年 / 248卷
关键词：
General Setting; Probability Theory; Essential Property; Unify Method; Exchangeability System;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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 various q-cumulants.
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页码：67 / 100
页数：33
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