统计意义下的Erdelyi-Kober分数次积分算子- III
Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -III
摘要：
本文定义了多元情形下的Kober分数次积分算子。首先考虑一个独立随机变量序列和一个任意函数，该函数可以作为另一个随机变量序列的联合密度。然后，我们定义了一个概念，类似于在标量变量情况下的Kober算子的概念。这种扩展是通过使用统计技术实现的，并且表示给出了联合统计密度方面的解释。然后我们看两组随机变量，在这两组变量之间，它们是独立分布的，但在每一组变量内部，它们是相关的。再次考虑Kober分数次积分算子的扩张.几个这样的统计解释给出了Kober算子在多变量的情况下。
英文摘要：
In this article we define Kober fractional integral operators in the multivariable case. First we consider one sequence of independent random variables and an arbitrary function, which can act as the joint density of another sequence of random variables. Then we define a concept, analogous to the concept of Kober operators in the scalar variable case. This extension is achieved by using statistical techniques and the representation gives an interpretation in terms of a joint statistical density. Then we look at two sets of random variables where between the sets they are independently distributed but within each set they are dependent. Again extensions of Kober fractional integral operator are considered. Several such statistical interpretations are given for Kober operators in the multivariable case.
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