Loeb 空间上的拟鞅提升及分解定理

本文通过非标准随机分析方法得到了标准拟鞅提升定理，并构造了非标准拟鞅的分解定理，然后再通过下推方法得到了标准拟鞅的一个分解定理。

A Lifting and Decomposing Theorem for Quasi-Martingales On the Loeb Space

In this paper,we obtain a lifting theorem for standard quasi-martingales by the nonstandard stochastic analysis at first,and construct a decomposing theorem for nonstandard quasi-martingales,and then obtain a decomposing theorem for standard quasimartingales by the pushing-down method.