随机元的稳弱收敛

证明了取值于Polish空间的稳弱收敛随机元列,在加大概率空间时,必存在极限,其次,对Jacod提出的弱收敛必是稳弱收敛相对紧证明有缺陷作了补正。

Stably Weak Convergence of Random Elements

At first,this paper demonstrates the existence of limit in an extended probability space for the stably weak convergence sequence of random elements which take values in a Polish space. And secondly, it is shown that the weak convergent sequence of random elements is ralatively compact in a stably weak convergence. This conclusion was proved by Jacod and Memin in Lecture Note Math 850, Springer(1981) 529-546, but they used the incorrect conclusion-the Banach space of uniformly continuous functions is separable. Thirdly, some related conclusions are obtained.