集值鞅的Doob停止定理  

Doob stopping theorem of setvalued martingales

作　　者：陈新香[1] 越觐周 

机构地区：[1]陕西师范大学数学系

出　　处：《陕西师大学报（自然科学版）》1998年第2期25-28,共4页Journal of Shaanxi Normal University(Natural Science Edition)

摘　　要：设｛Ｆｎ，ｎ≥１｝是Ｌ１ｆｃ［Ω；Ｘ］值鞅（上鞅，下鞅），首先以支撑函数为工具，对有界停时证明了Ｄｏｏｂ停止定理，然后将结果推广到更一般的场合．对可闭集值鞅（上鞅），Ｄｏｏｂ停止定理对一切停时成立；而对一般的集值鞅（上鞅），此时Ｄｏｏｂ停止定理只对某些停时成立；最后将上述结论推广到连续时间集值鞅上．Let{Fn, n≥1} is L1fcvalued martingales (supermartingales, submartingales). The first Doob′s stopping theorem for bounded stopping times is proved. Then the result is generalized to more general cases: one is to a class of closable setvalued martingales (supermartingales), at this time Doob′s stopping theorem holds for all stopping times; the other is to general setvalued martingales (supermartingales), in this case Doob′s stopping theorems hold only for certain stopping times. At last all the results are generalized to the setvalued martingales with continuous time.

关 键 词：集值鞅 停时 支撑函数 Doob停止定理 随机集 

分 类 号：O211.6[理学—概率论与数理统计]