随机元的稳弱收敛

Stably Weak Convergence of Random Elements

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。

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.