ON THE NON-CLASSICAL INFINITE DIVISIBILITY OF POWER SEMICIRCLE DISTRIBUTIONS
ON THE NON-CLASSICAL INFINITE DIVISIBILITY OF POWER SEMICIRCLE DISTRIBUTIONS
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论幂半圆分布的非经典无限可分性
DOI：
10.31390/cosa.4.2.03
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
V. Pérez
中科院分区：
文献类型：
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作者：
Octavio Arizmendi;V. Pérez
研究了幂循环分布族，定义为循环密度的正规化真实的幂.高维欧氏空间中球面上均匀分布的边值都包含在这个族中，边界情形是经典的高斯分布。回顾了一些结果，包括成因和所谓的庞加莱定理。这些分布的矩与超Catalan数有关，并导出了它们的Cauchy变换。这类分布中的一些成员在非交换概率的加性卷积中扮演高斯分布的角色，例如自由卷积、单调卷积、反单调卷积和布尔卷积。使用简单的峰度参数研究了其他幂循环分布相对于这些卷积的无限可分性。发现了峰度与自由整除指标之间的联系，证明了对于经典高斯分布，自由整除指标严格小于2。
The family of power semicircle distributions defined as normal- ized real powers of the semicircle density is considered. The marginals of uniform distributions on spheres in high-dimensional Euclidean spaces are included in this family and a boundary case is the classical Gaussian dis- tribution. A review of some results including a genesis and the so-called Poincare's theorem is presented. The moments of these distributions are re- lated to the super Catalan numbers and their Cauchy transforms in terms of hypergeometric functions are derived. Some members of this class of dis- tributions play the role of the Gaussian distribution with respect to additive convolutions in non-commutative probability, such as the free, the monotone, the anti-monotone and the Boolean convolutions. The infinite divisibility of other power semicircle distributions with respect to these convolutions is stud- ied using simple kurtosis arguments. A connection between kurtosis and the free divisibility indicator is found. It is shown that for the classical Gaussian distribution the free divisibility indicator is strictly less than 2.
通过乘法重正化表征一类概率测度
DOI：
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发表时间：
2007
期刊：
Communications on Stochastic Analysis 1・3
影响因子：
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作者：
Hidetaka Hamada;Tatsuhiro Honda;Gabriela Kohr;Izumi Kubo
通讯作者：
Izumi Kubo
切比雪夫多项式和交互福克空间的插值
DOI：
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发表时间：
2006
期刊：
Infinite Dimensional Analysis, Quantum Probability and Related Topics 9(3)
影响因子：
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作者：
Hidetaka Hamada;Tatsuhiro Honda;Gabriela Kohr;Izumi Kubo;Hisashi Yokota;Hidetaka Hamada;Nobuhiro Asai;Toshio Nakata;Izumi Kubo
通讯作者：
Izumi Kubo