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Taboo rate and hitting time distribution of continuous-time reversible Markov chains

Author

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  • Xiang, Xuyan
  • Fu, Haiqin
  • Zhou, Jieming
  • Deng, Yingchun
  • Yang, Xiangqun

Abstract

The taboo rate is first defined, which satisfies with the Chapman–Kolmogorov equation. Then the differentials of hitting time distribution are expressed by many different taboo rates, which deeply reveal the intrinsic relationship between the transition rate matrix and the hitting time distribution in continuous-time reversible Markov chains. As an example, the explicit expressions of the differentials of the hitting time distribution at a single state are provided for the birth and death chain, hence the transition rate matrix can be identified. Such differentials improve the theory of statistical identification of continuous-time reversible Markov chains.

Suggested Citation

  • Xiang, Xuyan & Fu, Haiqin & Zhou, Jieming & Deng, Yingchun & Yang, Xiangqun, 2021. "Taboo rate and hitting time distribution of continuous-time reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:stapro:v:169:y:2021:i:c:s0167715220302728
    DOI: 10.1016/j.spl.2020.108969
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    References listed on IDEAS

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    1. Xuyan Xiang & Xiao Zhang & Xiaoyun Mo, 2018. "Statistical Identification of Markov Chain on Trees," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-13, March.
    2. Emilio De Santis & Fabio Spizzichino, 2016. "Some Sufficient Conditions for Stochastic Comparisons Between Hitting Times for Skip-free Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1021-1034, December.
    3. Wenming Hong & Ke Zhou, 2017. "A note on the passage time of finite-state Markov chains," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 438-445, January.
    4. Bulinskaya, Ekaterina Vladimirovna, 2014. "Finiteness of hitting times under taboo," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 15-19.
    5. Albrecher, Hansjorg & Boxma, Onno J., 2005. "On the discounted penalty function in a Markov-dependent risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 650-672, December.
    6. Zhou, Ke, 2013. "Hitting time distribution for skip-free Markov chains: A simple proof," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1782-1786.
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