林娜, 刘源远. 连续时间马氏链的代数及指数非常返性[J]. 应用概率统计, 2022, 38(4): 546-562. DOI: 10.3969/j.issn.1001-4268.2022.04.005
引用本文: 林娜, 刘源远. 连续时间马氏链的代数及指数非常返性[J]. 应用概率统计, 2022, 38(4): 546-562. DOI: 10.3969/j.issn.1001-4268.2022.04.005
shu
LIN Na, LIU Yuanyuan. On Algebraic and Exponential Transience for Continuous-Time Markov Chains[J]. Chinese Journal of Applied Probability and Statistics, 2022, 38(4): 546-562. DOI: 10.3969/j.issn.1001-4268.2022.04.005
Citation: LIN Na, LIU Yuanyuan. On Algebraic and Exponential Transience for Continuous-Time Markov Chains[J]. Chinese Journal of Applied Probability and Statistics, 2022, 38(4): 546-562. DOI: 10.3969/j.issn.1001-4268.2022.04.005
shu

连续时间马氏链的代数及指数非常返性

On Algebraic and Exponential Transience for Continuous-Time Markov Chains

    摘要
  • 摘要: 本文研究了连续时间马氏链的代数非常返性和指数非常返性,揭示了连续时间马氏链与其跳跃链和对偶过程之间的等价关系. 运用所得结果,我们进一步得到了广义分支过程和生灭过程等连续时间马氏链的非常返性判别准则.

     

    Abstract: In this paper, we investigate algebraic and exponential transience for continuous-time Markov chains (CTMCs). Equivalent relations of these transience are revealed between CTMCs and their jump chains and dual processes. The results are further applied to derive the criteria of these transience for general CTMCs, generalized Markov branching processes and birth-death processes.

     

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