Convergence of set valued sub- and supermartingales in the Kuratowski-Mosco sense

• 成果类型: Article
• 署名作者: Li, SM; Ogura, Y
• 署名单位: Saga University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 1384-1402
• 关键词: conditional expectations; random-variables; large numbers; martingales; MULTIFUNCTIONS; THEOREMS

摘要

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.