| 关于可列非齐次马氏链的若干极限定理 |
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| 引用本文： | 吴玉,范爱华.关于可列非齐次马氏链的若干极限定理[J].纯粹数学与应用数学,2015(2):182-193. |
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| 作者姓名： | 吴玉 范爱华 |
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| 作者单位： | 安徽工业大学数理科学与工程学院,安徽 马鞍山,243032 |
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| 基金项目： | 安徽工业大学青年教师科研基金，安徽省自然科学基金，安徽工业大学研究生创新基金 |
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| 摘 要： | 设{Xn,n≥0}是一列非齐次马尔科夫链,{an,n≥0}是一列固定的非负整数序列.首先构造了一个带参数的广义似然比函数,然后利用Borel-Cantelli引理证明随机变量序列几乎处处收敛性,得到了关于可列非齐次马氏链序偶广义平均的若干极限定理,推广了已有的结果.
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| 关 键 词： | 可列非齐次马氏链 B-C引理 强大数定律 |
Some limit theorems for non-homogeneous Markov chains |
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| Wu Yu,Fan Aihua.Some limit theorems for non-homogeneous Markov chains[J].Pure and Applied Mathematics,2015(2):182-193. |
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| Authors: | Wu Yu Fan Aihua |
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| Institution: | Wu Yu;Fan Aihua;School of Mathematics & Physics Science and Engineering, Anhui University of Technology; |
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| Abstract: | Let {Xn, n ≥ 0} be a sequence of nonhomogeneous Markov chains and {an, n ≥ 0} be a fixed sequence of non-negative integers. In this paper, we first construct a generalized likelihood ratio function with a parameter, then by using the Borel-Cantelli Lemma to prove the almost everywhere convergence of random variables, we obtain some limit theorems for countable nonhomogeneous Markov chains of ordered couple of generalized mean, which generalize some existing results. |
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| Keywords: | nonhomogeneous Markov chain B-C Lemma strong law of large numbers |
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