椭球等高过程及其性质

Process of the Ellipsoidal Equal Height and its Properties

本文从椭球等高分布族出发研究一类新的随机过程——椭球等高过程。它是用一个具有相当广泛意义的特征函数定义的。由此,证明了一个随机过程是椭球等高过程的充分必要条件是它的任意有限个元素的线性组合是一维椭球等高变量。并证明了它具有类似于正态过程的两个优良性质:(1)由该过程所张成的线性集也是椭球等高过程;(2)在依概率收敛的意义下,该过程的闭包也是椭球等高过程。

In this paper,we study a new kind of stochastic process from the family of distribution of ellipsoidal equal height, that is, the process of ellipsoidal equal height. It is defined by a characteristic function which has a rathar wide meaning. Starting from here we proved the sufficient and necessary condition of which the stochastic process is ellipsoidal equal height, is that the linear combination of arbitrary limited elements of this process is one-dimension of variable of ellipsoidal equal height, and we proreds that this process has two fine properties similar to Normal process: (1) The linear set generated by this process is also the process of ellipsoidal equal height. (2) Under the meaning of convergence in probability the closure of this process is also the process of ellipsoidal equal height.