| 随机环境中的马氏链的不变测度与遍历性 |
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| 引用本文： | 肖争艳.随机环境中的马氏链的不变测度与遍历性[J].数学杂志,2003,23(1):19-24. |
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| 作者姓名： | 肖争艳 |
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| 作者单位： | 武汉大学数学与统计学院,武汉,430072 |
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| 基金项目： | Supported by N.A.S.F of China，Fundation of Wuhan University |
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| 摘 要： | 本文考虑了一类特殊的随机环境的马氏链。假设随机“Doeblin”条件成立，我们证明了随机环境的马氏链的不变测度存在，且任何初始分布以指数收敛速度到些不变测度。进一步的，存在关于绕积算子遍历的不变测度。最后，我们得到了随机马氏链的强大数定律。
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| 关 键 词： | 马氏链 随机环境 不变测度 遍历定理 |
THE INVARIANT MEASURE AND ERGODICITY OF MARKOV CHAINS IN RANDOM ENVIRONMENTS |
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| XIAO Zheng-yan.THE INVARIANT MEASURE AND ERGODICITY OF MARKOV CHAINS IN RANDOM ENVIRONMENTS[J].Journal of Mathematics,2003,23(1):19-24. |
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| Authors: | XIAO Zheng-yan |
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| Abstract: | In this paper, we consider a particular case of Markov chains in random environments. Suppose that the random Doeblin condition is satisfied, we prove that the invariant measure exists and any initial distibution convergence to the measure with an exponential rate. Furthmore, we calaim that there is an invariant measure ergodic for the skew product operator. At last, as an application, we obtain the law of large numbers for Markov chains in random environments. |
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| Keywords: | Markow chains random environment invariant measure ergodic theorem |
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