Assembly Method Constructing Dependent Random Variables Using Independent Product Space

An assembly method of constructing dependent random variables or dependent random processes by using independent product space is given.Firstly independent random variables according to the given conditions are constructed,and then independent random variables are assembled and required dependent random variables are obtained.The advantages of this method are: the joint distribution or the family of finite-dimensional distributions is not calculated when the dependent random variables or dependent random processes are wanted to construct;more convenient and simple approach about independent random variables can be used as the dependent random variables or dependent random processes are studied;moreover the probabilistic construction proof about existence of some random processes can be given.