关于停线的停止定理

Stopping theorem for stopping line

关于停线的停止定理赵觐周１陈慧婵２张卓奎２（１陕西师范大学数学系，西安７１００６２；２西北轻工业学院基础课部，陕西咸阳，７１２０８１；第一作者，男，６３岁，教授）Ｅ．Ｍｅｒｚｂａｃｈ在文〔１〕中曾研究了强鞅关于有界停线的停止定理，但是，庄兴无和Ｚｂａ...

The stopping problem for stopping line is studied, two theorems are proved. With theorem 1(stopping theorem), let M be strong martingales, M(s,0)=M(0,t) =0, then for any bounded stopping line λ and μ, λ≤μ , there is E(M μ|F λ)= M λ, a.s. With theorem 2 (Previsible stopping theorem ), let M be strong martingales, M(s.0)=M(0,t) =0, then for any bounded previsible stopping line λ and bounded stopping line μ, λ<μ, there is E( M μ|F λ- )= M λ- a.s. These results revise and extend Merzbach′s stopping theorem for stopping line.