| 关于树指标二重非齐次马氏链的强极限定理 |
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| 引用本文： | 杨卫国,云广亮.关于树指标二重非齐次马氏链的强极限定理[J].江苏大学学报(自然科学版),2012,33(4):486-490. |
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| 作者姓名： | 杨卫国 云广亮 |
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| 作者单位： | 江苏大学 理学院,江苏 镇江,212013 |
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| 基金项目： | 国家自然科学基金资助项目(11071104) |
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| 摘 要： | 研究树上二重非齐次马氏链随机转移概率的几何平均强极限定理和二重非齐次马氏链关于状态出现频率的强极限定理.首先引出了二重非齐次马氏链的概念,然后给出了一个引理,利用这个引理,建立了双根树上二重非齐次马氏链随机转移概率的用不等式表示的几何平均强极限定理,接着推出了二重非齐次马氏链关于状态序偶出现频率的用不等式表示的强极限定理;最后作为推论,得到树上有限非齐次马氏链随机转移概率的强极限定理.
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| 关 键 词： | 树 二重非齐次马氏链 随机转移概率 几何平均 状态出现频率 |
Strong limit theorems for second-order nonhomogeneous Markov chains indexed by a tree |
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| Yang Weiguo
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Yun Guangliang.Strong limit theorems for second-order nonhomogeneous Markov chains indexed by a tree[J].Journal of Jiangsu University:Natural Science Edition,2012,33(4):486-490. |
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| Authors: | Yang Weiguo Yun Guangliang |
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| Institution: | (Faculty of Science,Jiangsu University,Zhenjiang,Jiangsu 212013,China) |
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| Abstract: | Some strong limit theorems relative to the geometric average of random transition probability for second-order nonhomogeneous Markov chains indexed by a tree were studied.The definition of the se-cond-order nonhomogeneous Markov chains was introduced to propose a lemma.According to the lemma,some strong limit theorems relative to the geometric average of random transition probability with inequality for second-order nonhomogeneous Markov chains indexed by a tree were established.Some strong limit theorems relative to occasional occurred frequency of states with inequality for second-order nonhomogeneous Markov chains indexed by a tree were deduced.As corollaries,some strong limit theorems for finite nonhomogeneous Markov chains indexed by a tree were achieved. |
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| Keywords: | tree second-order nonhomogeneous Markov chains random transition probability geometric average occurred frequency of states |
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