论文标题
1--粘合剂随机向量
1--Meixner random vectors
论文作者
论文摘要
$ d $的定义 - 尺寸$ n $ - Meixner随机向量首先给出。该定义涉及其半量子运算符的换向器。之后，我们将重点关注$ 1 $ -Meixner随机向量，并得出由$ d $ partial微分方程的系统，其拉普拉斯变换满足。我们为该系统提供了一组必要条件。我们使用这些条件对所有非降级三维$ 1 $ - meixner随机向量进行完整表征。必须提到的是，三维情况会产生第一个示例，其中$ 1 $的组件 - Meixner随机向量无法通过注入式线性变换减少到三个独立的经典Meixner随机变量。
A definition of $d$--dimensional $n$--Meixner random vectors is given first. This definition involves the commutators of their semi--quantum operators. After that we will focus on the $1$-Meixner random vectors, and derive a system of $d$ partial differential equations satisfied by their Laplace transform. We provide a set of necessary conditions for this system to be integrable. We use these conditions to give a complete characterization of all non--degenerate three--dimensional $1$--Meixner random vectors. It must be mentioned that the three--dimensional case produces the first example in which the components of a $1$--Meixner random vector cannot be reduced, via an injective linear transformation, to three independent classic Meixner random variables.
