集值随机分析中的完备性问题

Completeness of set-valued stochastic analysis

定义了一个由可料紧凸集值随机过程构成的空间和两个可料紧凸集值随机过程的距离 ,并给出了两随机过程相等的条件 ,由此空间以及定义在其上的距离 ,构造了一个度量空间 ,并证明了这个度量空间是完备的。进而给出了一个由平方可积紧凸集值鞅构成的度量空间 ,说明了这个空间也是完备的。

A space based on predicted convex set valued stochastic processes was presented firstly, a distance was defined, a condition under which two stochastic processes are equal was offered. The space was proved complete. A space based on square integral convex set valued martingale was introduced. That the space is complete is viewed, which will play an important part in the deeper research of set valued stochastic analysis.