Convergence of set valued sub- and supermartingales in the Kuratowski-Mosco sense
Convergence of set valued sub- and supermartingales in the Kuratowski-Mosco sense
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DOI：
10.1214/aop/1022855757
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发表时间：
1998-07
影响因子：
2.3
通讯作者：
Shoumei Li;Y. Ogura
中科院分区：
文献类型：
--
作者：
Shoumei Li;Y. Ogura
本文证明了在Kuratowski-Mosco意义下闭凸集值下鞅和上鞅的一些收敛定理。为了得到下鞅收敛定理，我们给出了紧凸集值随机变量和闭凸集值随机变量的Kudo-Aumann积分和Hiai-Umegaki条件期望为闭的充分条件.给出了一个有界闭凸集值随机变量的Kudo-Aumann积分不闭的例子。
The purpose of this paper is to prove some convergence theorems of closed and convex set valued sub- and supermartingales in the Kuratowski-Mosco sense. To get submartingale convergence theorems, we give sufficient conditions for the Kudo-Aumann integral and Hiai-Umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables. We also give an example of a bounded closed convex set valued random variable whose Kudo-Aumann integral is not closed.