识别独立随机过程的一个充要条件

Necessary and Sufficient Condition for Identifying Independent Random Processes

识别独立随机过程的一个充要条件是独立随机过程的有限维概率密度函数,可表示为若干个一维函数的乘积,这些一维函数只与相对应的边缘概率密度函数相差一个常数,且其中有关的边界常数均与自变量和参数无关.这是独立随机过程的有限维概率密度函数的2个特征,利用此特征可以避免求有限维边缘概率密度函数,使判定随机过程是否独立随机过程的工作变得非常简单.

A necessary and sufficient condition for an identifying independent random process is that the finitedimensional probability density function of the process can be expressed with a product of some onedimensional functions. The only difference between the onedimensional functions and the corresponding marginal density function is a constant, and the boundary constants are irrelevant with variables and parameters. Those are two important characters of density functions of independent random processes. Using those characters to avoid solving the marginal density function makes the identification of an independence of random process simple.