关于自然提升过程的一个新的应用

文1]中提出了可测空间的自然乘积空间和随机过程的自然提升过程等概念,并且证明了一个随机过程循序可测的充分必要条件是其自然提升过程是适应过程.在此基础上,找到了可料过程与自然提升过程之间的关系,并且把自然提升过程引入到了可及过程当中,得出了自然提升过程是适应过程的另一个充分必要条件.

A New Application of the Natural-lifting Process

In text 1 ] notions are introduced firstly of the natural - product space of a measurable space and of the natural - lifting process of a stochastic process as well as of others. And then it is proved that a process is progressively measurable if and only if its natural- lifting process is adapted. On this basis, the paper finds the relations between predictable process and natural - lifting process, and applies the concept of natural - lifting process to accessible process. Except this, the paper reaches another sufficient and necessary condition about natural- lifting process is adapting process.