| 三元树上非对称马氏链场的强大数定律 |
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| 引用本文： | 杨卫国,宋玉琴. 三元树上非对称马氏链场的强大数定律[J]. 江苏大学学报(自然科学版), 2007, 28(6): 549-552 |
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| 作者姓名： | 杨卫国 宋玉琴 |
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| 作者单位： | 江苏大学,理学院,江苏,镇江212013;湖南工业大学,理学院,湖南,株洲,412008 |
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| 摘 要： | 定义了一类三元树上非对称马尔可夫链场, 利用鞅方法构造鞅, 根据Doob鞅收敛定理和一些特殊的不等式以及近年来研究概率论强极限定理的新方法,研究了三元树上非对称马尔可夫链场的强极限定理以及关于状态和状态序偶出现频率的强大数定理, 得到了三元树上非对称马尔可夫链场的局部收敛定理以及关于状态和状态序偶出现频率的强大数定理, 将三元树上对称马氏链场中的相关结果推广到了三元树上非对称马氏链场中.
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| 关 键 词： | 非对称树马氏链场 树 鞅 状态序偶 强大数定律 |
| 文章编号： | 1671-7775（2007）06-0549-04 |
| 修稿时间： | 2006-12-08 |
Strong law of large numbers for non-symmetric Markov chain field on a three branches tree |
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| YANG Wei-guo,SONG Yu-qin. Strong law of large numbers for non-symmetric Markov chain field on a three branches tree[J]. Journal of Jiangsu University:Natural Science Edition, 2007, 28(6): 549-552 |
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| Authors: | YANG Wei-guo SONG Yu-qin |
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| Affiliation: | 1. Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China; 2. College of Science, Hunan University of Technology, Zhuzhou, Hunan 412008, China |
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| Abstract: | The definition of a non-symmetric Markov chain field is given. By applying Martingale and Doob Martingale convergence theorems, some special inequalities and a new technique for establishing the strong limit theorems, the strong limit theorems for non-symmetric Markov chain field on a three branches tree are studied. A local convergence theorem and the strong law of large numbers for non-symmetric Markov chain field are obtained. Some results about the symmetric Markov chain field are extended to the non-symmetric case. |
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| Keywords: | non-symmetric Markov chain field tree Martingale ordered couple of states strong law of large number |
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