论文标题
随机向量的高阶张量矩
High order tensor moments of random vectors
论文作者
论文摘要
随机向量$ \ bx \ in \ r^n $是一个向量，其坐标都是随机变量。如果随机向量遵循高斯分布，则称为高斯向量。这些术语也可以扩展到随机（高斯）基质和随机（高斯）张量。随机向量$ \ bx \ in \ r^n $的$ k $ ordorm时刻（对于任何积极整数$ k $）通常以$ n \ times n^{k-1} $的矩阵形式表示，从$ n分布式向量。使用张量形式，我们可以简化与高阶矩相关的所有表达式。本文的主要目的是以张量形式引入随机向量的高阶力矩和标准正常分布式向量的高阶矩。最后，我们提出了随机向量的高阶力矩的表达，该载体跟随高斯分布。
A random vector $\bx\in \R^n$ is a vector whose coordinates are all random variables. A random vector is called a Gaussian vector if it follows Gaussian distribution. These terminology can also be extended to a random (Gaussian) matrix and random (Gaussian) tensor. The classical form of an $k$-order moment (for any positive integer $k$) of a random vector $\bx\in \R^n$ is usually expressed in a matrix form of size $n\times n^{k-1}$ generated from the $k$th derivative of the characteristic function or the moment generating function of $\bx$ , and the expression of an $k$-order moment is very complicate even for a standard normal distributed vector. With the tensor form, we can simplify all the expressions related to high order moments. The main purpose of this paper is to introduce the high order moments of a random vector in tensor forms and the high order moments of a standard normal distributed vector. Finally we present an expression of high order moments of a random vector that follows a Gaussian distribution.
