祝东进. 随机环境中马氏链的平稳分布[J]. 应用概率统计, 2012, 28(4): 337-344.
引用本文: 祝东进. 随机环境中马氏链的平稳分布[J]. 应用概率统计, 2012, 28(4): 337-344.
Zhu Dongjin. The Stationary Distribution of Markov Chains in Random Environments[J]. Chinese Journal of Applied Probability and Statistics, 2012, 28(4): 337-344.
Citation: Zhu Dongjin. The Stationary Distribution of Markov Chains in Random Environments[J]. Chinese Journal of Applied Probability and Statistics, 2012, 28(4): 337-344.

随机环境中马氏链的平稳分布

The Stationary Distribution of Markov Chains in Random Environments

  • 摘要: 本文引入了随机环境中马氏链平稳分布的概念. 在合适的条件下, 给出了随机环境中马氏链的平稳分布存在的一些充分条件. 特别地, 讨论了Cogburn链的平稳分布存在性问题. 同时, 构造了一个随机环境中马氏链的例子, 它的平稳分布是存在的.

     

    Abstract: In this paper, the concept of stationary distribution of Markov chains in random environments (MCIRE) is introduced, and basic properties of MCIRE are discussed. It is shown that there exists a stationary distribution of MCIRE under some natural conditions. In particular, the existence of stationary distribution of Cogburn's chain are discussed. Moreover, we give an example of MCIRE which stationary distribution exists.

     

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