| 任意随机序列的变换及其a.s.收敛性 |
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| 引用本文： | 汪忠志,刘文.任意随机序列的变换及其a.s.收敛性[J].数学杂志,2005,25(5):513-520. |
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| 作者姓名： | 汪忠志 刘文 |
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| 作者单位： | 1. 安徽工业大学数理学院,安徽,马鞍山,243002
2. 河北工业大学理学院,天津,300130 |
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| 基金项目： | Supported by Anhui-High Educational Research Grant（2004Kj069） |
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| 摘 要： | 本文利用截尾方法构造几乎处处收敛的鞅结合无穷乘积定理，研究随机变量序列变换的局部收敛性及强大数定理，作为推论得到了关于赌博系统的若干强极限定理。
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| 关 键 词： | 变换 鞅 局部收敛 a．s．收敛 赌博系统 |
| 文章编号： | 0255-7797（2005）05-0513-08 |
| 收稿时间： | 2003-05-26 |
| 修稿时间： | 2003-05-262004-06-07 |
RANDOM TRANSFORMS FOR ARBITRARY STOCHASTIC SEQUENCE AND a.s. CONVERGENCE |
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| WANG Zhong-Zhi,LIU Wen.RANDOM TRANSFORMS FOR ARBITRARY STOCHASTIC SEQUENCE AND a.s. CONVERGENCE[J].Journal of Mathematics,2005,25(5):513-520. |
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| Authors: | WANG Zhong-Zhi LIU Wen |
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| Abstract: | In this paper, we discuss the convergence of the random transform for arbitrary stochastic sequence. Furthermore, by means of martingale convergence theorem together with the theorem of infinite products, we prove some limit theorems concerning local convergence of such transforms and strong law of large numbers. At last, as a consequence, we obtain some strong law of large numbers on gambling system. |
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| Keywords: | transform martingales local convergence a s convergence gambling system |
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