Free Infinite Divisibility of Free Multiplicative Mixtures of the Wigner Distribution
Free Infinite Divisibility of Free Multiplicative Mixtures of the Wigner Distribution
复制标题
维格纳分布的自由乘法混合的自由无限整除性
DOI：
10.1007/s10959-010-0288-5
复制
发表时间：
2010
影响因子：
0.8
通讯作者：
Noriyoshi Sakuma
中科院分区：
文献类型：
--
作者：
V. Pérez;Noriyoshi Sakuma
设I * 和I分别是所有经典无穷可分分布和自由无穷可分分布的类，设Λ是I * 和I之间的Bercovici-Pata双射.研究了可表示为Wigner分布的自由乘卷积的I中对称分布的类W。在混合分布关于自由乘卷积是2-可分的条件下，给出了这类卷积的一个刻划。建立了I * 中正分布的对称分布与在Λ下的自由分布之间的对应关系。证明了类类型W并不包括I * 中的所有对称分布，并且它与I * 中高斯分布的混合在Λ下的象也不一致.对具有对称反正弦测度的自由乘卷积也得到了类似的结果。几个著名的和新的具体的例子。
LetI*andI⊞be the classes of all classical infinitely divisible distributions and free infinitely divisible distributions, respectively, and letΛbe the Bercovici–Pata bijection betweenI*andI⊞. The class typeWof symmetric distributions inI⊞that can be represented as free multiplicative convolutions of the Wigner distribution is studied. A characterization of this class under the condition that the mixing distribution is 2-divisible with respect to free multiplicative convolution is given. A correspondence between symmetric distributions inI⊞and the free counterpart underΛof the positive distributions inI*is established. It is shown that the class typeWdoes not include all symmetric distributions inI⊞and that it does not coincide with the image underΛof the mixtures of the Gaussian distribution inI*. Similar results for free multiplicative convolutions with the symmetric arcsine measure are obtained. Several well-known and new concrete examples are presented.
某些类无限可分分布允许随机积分表示
DOI：
--
发表时间：
2006
期刊：
Bernoulli Vol.12, No.1
影响因子：
--
作者：
O.E.Barndorff-Nielsen;M.Taejima;K.Sato
通讯作者：
K.Sato