| 弱集值渐近鞅的收敛定理 |
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| 引用本文： | 刘常昱,李世楷,严榴香.弱集值渐近鞅的收敛定理[J].解放军理工大学学报,2001,2(3):99-102. |
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| 作者姓名： | 刘常昱 李世楷 严榴香 |
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| 作者单位： | 解放军理工大学理学院 江苏南京211101
(刘常昱，李世楷)，解放军理工大学理学院 江苏南京211101(严榴香) |
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| 摘 要： | 为了得到关于弱集值渐近鞅的收敛性质，首先证明了支撑数列的极限亦为一支撑函数，利用支撑函数的性质以及 值鞅的Doob停止定理，证明得到了两个结论：（1）在一定条件下，弱值值渐近鞅存在无限逼近的闭凸集值鞅；（2）在弱收敛意义下，弱值值渐近鞅收敛的两个等价条件。
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| 关 键 词： | 弱集值渐近鞅 弱收敛 支撑函数 鞅逼近 Doob停止定理 闭凸集值鞅 收敛定理 |
| 文章编号： | 1009-3443（2001）03-0099-04 |
Convergence Theorem of the Weak Set -valued Amart |
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| LIU Chang-yu,LI Shi-kai and YAN Liu-xiang.Convergence Theorem of the Weak Set -valued Amart[J].Journal of PLA University of Science and Technology(Natural Science Edition),2001,2(3):99-102. |
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| Authors: | LIU Chang-yu LI Shi-kai and YAN Liu-xiang |
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| Institution: | Institute of Sciences, PLA Univ. of Sci. & Tech., Nanjing 211101, China;Institute of Sciences, PLA Univ. of Sci. & Tech., Nanjing 211101, China;Institute of Sciences, PLA Univ. of Sci. & Tech., Nanjing 211101, China |
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| Abstract: | In order to get the convergence properties of the weak set-valued Amart, we firstly proved the theorem that the limit of support functions is a support function. Based on the properties of support functions and the Doob's stopping theorem of the closed convex set-valued Amart, the following results are proved. Firstly, in certain conditions, there exists a set-valued Martingale approach to a weak set-valued Amat. Secondly, the convergence theorems of the weak set-valued Amart can be replaced by two equivalent conditions. |
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| Keywords: | weak set-valued Amart weak convergence support function martingales approach |
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