集值Pramart的鞅分解

The martingale decomposition for set-valued pramart

研究了集值Pramart的若干性质,利用支撑函数得到了集值Pramart的收敛定理,同时,证明了实值Pramart的鞅分解定理.以此为基础,给出了集值Pramart在Kuratowski-Mosco意义下的鞅分解定理.

The paper use support function, we show convercence theorem. The properties of set-valued pramart are also discussed, we get the martingale decomposition of a real-valued pramart {xn,n≥1} with lim n E ｜xn｜〈∞. At the end of this paper, we show that a set-valued pramart {Fn,n≥1} with lim E｜｜Fn｜｜ 〈∞ can be written Fn=Gn＋Zn,where {Gn,n≥1} is a martingale and where {Zn,n≥1} is a set-valued pramart while tend-to zero in terms of Kuratowski-Mosco a.s. （i. e Zn→ K-M {0}） .