IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v169y2021ics0167715220302728.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220302728
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2020.108969?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Bulinskaya, Ekaterina Vladimirovna, 2014. "Finiteness of hitting times under taboo," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 15-19.
    3. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang, Hu & Zhang, Zhimin & Lan, Chunmei, 2009. "Ruin problems in a discrete Markov risk model," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 21-28, January.
    2. Landriault, David & Shi, Tianxiang, 2015. "Occupation times in the MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 75-82.
    3. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    4. Jiang, Wuyuan & Yang, Zhaojun & Li, Xinping, 2012. "The discounted penalty function with multi-layer dividend strategy in the phase-type risk model," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1358-1366.
    5. 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.
    6. Feng, Runhuan, 2009. "On the total operating costs up to default in a renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 305-314, October.
    7. Franck Adékambi & Kokou Essiomle, 2021. "Asymptotic Tail Probability of the Discounted Aggregate Claims under Homogeneous, Non-Homogeneous and Mixed Poisson Risk Model," Risks, MDPI, vol. 9(7), pages 1-22, June.
    8. O. J. Boxma & M. R. H. Mandjes, 2022. "Queueing and risk models with dependencies," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 69-86, October.
    9. Hansjörg Albrecher & Eleni Vatamidou, 2019. "Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims," Risks, MDPI, vol. 7(4), pages 1-14, October.
    10. Lu, Yi & Li, Shuanming, 2009. "The Markovian regime-switching risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 296-303, April.
    11. David Landriault, 2008. "On a generalization of the expected discounted penalty function in a discrete‐time insurance risk model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(6), pages 525-539, November.
    12. Dickson, David C.M., 2012. "The joint distribution of the time to ruin and the number of claims until ruin in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 334-337.
    13. Cheung, Eric C.K. & Feng, Runhuan, 2013. "A unified analysis of claim costs up to ruin in a Markovian arrival risk model," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 98-109.
    14. Albrecher, Hansjörg & Constantinescu, Corina & Pirsic, Gottlieb & Regensburger, Georg & Rosenkranz, Markus, 2010. "An algebraic operator approach to the analysis of Gerber-Shiu functions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 42-51, February.
    15. Ehyter Matías Martín-González & Antonio Murillo-Salas & Henry Pantí, 2022. "Gerber-Shiu Function for a Class of Markov-Modulated Lévy Risk Processes with Two-Sided Jumps," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2779-2800, December.
    16. Li, Shuanming & Lu, Yi, 2009. "The distribution of total dividend payments in a Sparre Andersen model," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1246-1251, May.
    17. Xin Zhang, 2008. "On the Ruin Problem in a Markov-Modulated Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 225-238, June.
    18. Li, Jingchao & Dickson, David C.M. & Li, Shuanming, 2015. "Some ruin problems for the MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 1-8.
    19. Zhou, Ming & Cai, Jun, 2009. "A perturbed risk model with dependence between premium rates and claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 382-392, December.
    20. Zhou, Zhongbao & Xiao, Helu & Deng, Yingchun, 2015. "Markov-dependent risk model with multi-layer dividend strategy," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 273-286.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:169:y:2021:i:c:s0167715220302728. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.