IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v35y2022i3d10.1007_s10959-021-01105-5.html
   My bibliography  Save this article

Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains

Author

Listed:
  • Yong-Hua Mao

    (Ministry of Education)

  • Yan-Hong Song

    (Zhongnan University of Economics and Law)

Abstract

We present new criteria for geometric and algebraic transience for discrete-time transient Markov chains on general state spaces, based on the moment of the last exit time, the modified moment of the first return time and the drift condition for the transition kernel. These criteria turn out to be more convenient to use, supplementing and extending conditions introduced by Mao and Song [Stochastic Process. Appl. 124 (2014) 1648-1678]. Several applications are presented including discrete queueing Markov chains, Galton–Watson branching processes, downwardly skip-free chains, unrestricted random walks and autoregressive models of order one.

Suggested Citation

  • Yong-Hua Mao & Yan-Hong Song, 2022. "Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1974-2008, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01105-5
    DOI: 10.1007/s10959-021-01105-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-021-01105-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-021-01105-5?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. Nikola Sandrić, 2016. "Ergodic Property of Stable-Like Markov Chains," Journal of Theoretical Probability, Springer, vol. 29(2), pages 459-490, June.
    2. Mao, Yong-Hua & Song, Yan-Hong, 2014. "On geometric and algebraic transience for discrete-time Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1648-1678.
    3. Nummelin, Esa & Tuominen, Pekka, 1983. "The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 295-311, August.
    4. Wei, C. Z. & Winnicki, J., 1989. "Some asymptotic results for the branching process with immigration," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 261-282, April.
    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. Mika Meitz & Pentti Saikkonen, 2019. "Subgeometric ergodicity and $\beta$-mixing," Papers 1904.07103, arXiv.org, revised Apr 2019.
    2. Nikolaos Limnios & Elena Yarovaya, 2020. "Diffusion Approximation of Branching Processes in Semi-Markov Environment," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1583-1590, December.
    3. Robert Jung & Gerd Ronning & A. Tremayne, 2005. "Estimation in conditional first order autoregression with discrete support," Statistical Papers, Springer, vol. 46(2), pages 195-224, April.
    4. Mátyás Barczy & Kristóf Körmendi & Gyula Pap, 2016. "Statistical inference for critical continuous state and continuous time branching processes with immigration," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 789-816, October.
    5. Datta, Somnath & Sriram, T. N., 1995. "A modified bootstrap for branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 275-294, April.
    6. Song, Yan-Hong, 2016. "Algebraic ergodicity for SDEs driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 108-115.
    7. Huang, Jianhui & Ma, Chunhua & Zhu, Cai, 2011. "Estimation for discretely observed continuous state branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1104-1111, August.
    8. I. Rahimov, 2009. "Asymptotic distributions for weighted estimators of the offspring mean in a branching process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 568-583, November.
    9. Rahimov, I., 2011. "Estimation of the offspring mean in a supercritical branching process with non-stationary immigration," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 907-914, August.
    10. Phil Pollett, 2022. "Quasi-stationary distributions for queueing and other models," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 241-243, April.
    11. Mika Meitz & Pentti Saikkonen, 2022. "Subgeometrically ergodic autoregressions with autoregressive conditional heteroskedasticity," Papers 2205.11953, arXiv.org, revised Apr 2023.
    12. Kristóf Körmendi & Gyula Pap, 2018. "Statistical inference of 2-type critical Galton–Watson processes with immigration," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 169-190, April.
    13. Xu, Wei, 2014. "Parameter estimation in two-type continuous-state branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 124-134.
    14. Nummelin, Esa, 1997. "On distributionally regenerative Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 241-264, December.
    15. Meitz, Mika & Saikkonen, Pentti, 2022. "Subgeometrically Ergodic Autoregressions," Econometric Theory, Cambridge University Press, vol. 38(5), pages 959-985, October.
    16. Qi, Yongcheng & Reeves, Jaxk, 0. "On sequential estimation for branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 41-51, July.
    17. Barczy, M. & Ispány, M. & Pap, G., 2011. "Asymptotic behavior of unstable INAR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 583-608, March.
    18. Isabel Silva & M. Eduarda Silva & Isabel Pereira & Nélia Silva, 2005. "Replicated INAR(1) Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 517-542, December.
    19. Iksanov, Alexander & Meiners, Matthias, 2015. "Rate of convergence in the law of large numbers for supercritical general multi-type branching processes," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 708-738.
    20. Shete, Sanjay & Sriram, T. N., 1998. "Fixed precision estimator of the offspring mean in branching processes," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 17-33, September.

    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:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01105-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.