What is Stochastic Independence
What is Stochastic Independence
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什么是随机独立性
DOI：
10.1142/9789812705242_0008
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
U. Franz
中科院分区：
文献类型：
--
作者：
U. Franz
定义了具有投影或包含的张量积的概念。结果表明，随机独立性的定义依赖于这样的结构，并且独立性可以定义在具有包含或投影的张量积的任意范畴中。在这一背景下，Muraki、Ben Ghorbal和Sch-Urmann对量子随机独立性的分类成为代数概率空间和非么正代数概率空间范畴的包含张量积的分类.还引入了将一种独立性降低为另一种独立性的概念.作为例子，给出了费米独立性和布尔、单调和反单调独立性到张量独立性的简化.
The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor product with inclusions or projections. In this context, the classifications of quantum stochastic independence by Muraki, Ben Ghorbal, and Sch\"urmann become classifications of the tensor products with inclusions for the categories of algebraic probability spaces and non-unital algebraic probability spaces. The notion of a reduction of one independence to another is also introduced. As examples the reductions of Fermi independence and boolean, monotone, and anti-monotone independence to tensor independence are presented.