IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v192y2023ics016771522200205x.html
   My bibliography  Save this article

Domain of attraction of quasi-stationary distribution for absorbing Markov processes

Author

Listed:
  • Zhang, Hanjun
  • Mo, Yongxiang

Abstract

In this paper, for the general λ0-positive absorbing Markov processes, we obtain a concise result on the domain of attraction of the quasi-stationary distribution. Our conclusion includes some existing results. Finally, we apply our result to multi-dimensional Ornstein–Uhlenbeck process and give a subset of the domain of attraction of its minimal quasi-stationary distribution.

Suggested Citation

  • Zhang, Hanjun & Mo, Yongxiang, 2023. "Domain of attraction of quasi-stationary distribution for absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:stapro:v:192:y:2023:i:c:s016771522200205x
    DOI: 10.1016/j.spl.2022.109692
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771522200205X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2022.109692?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. He, Guoman & Zhang, Hanjun & Zhu, Yixia, 2019. "On the quasi-ergodic distribution of absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 116-123.
    2. Cohn, H. & Hering, H., 1983. "Inhomogeneous Markov branching processes: Supercritical case," Stochastic Processes and their Applications, Elsevier, vol. 14(1), pages 79-91, January.
    3. Breyer, L. A. & Roberts, G. O., 1999. "A quasi-ergodic theorem for evanescent processes," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 177-186, December.
    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. Oçafrain, William, 2020. "Q-processes and asymptotic properties of Markov processes conditioned not to hit moving boundaries," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3445-3476.
    2. He, Guoman & Zhang, Hanjun & Yang, Gang, 2021. "Exponential mixing property for absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 179(C).
    3. He, Guoman & Zhang, Hanjun, 2016. "On quasi-ergodic distribution for one-dimensional diffusions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 175-180.
    4. Sagitov, Serik, 2017. "Tail generating functions for extendable branching processes," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1649-1675.
    5. Liu, Rongli & Ren, Yan-Xia & Song, Renming, 2022. "Convergence rate for a class of supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 286-327.
    6. Ren, Yan-Xia & Song, Renming & Zhang, Rui, 2015. "Central limit theorems for supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 428-457.
    7. Mailler, Cécile & Mörters, Peter & Senkevich, Anna, 2021. "Competing growth processes with random growth rates and random birth times," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 183-226.
    8. Castro, Matheus M. & Lamb, Jeroen S.W. & Olicón-Méndez, Guillermo & Rasmussen, Martin, 2024. "Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: A Banach lattice approach," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    9. Daehong Kim & Takara Tagawa, 2025. "Quasi-Ergodic Limits for Moments of Jumps Under Absorbing Stable Processes," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-19, March.
    10. Liu, Rongli & Ren, Yan-Xia & Song, Renming & Sun, Zhenyao, 2021. "Quasi-stationary distributions for subcritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 108-134.
    11. Wang, Juan & Wang, Xueke & Li, Junping, 2023. "Asymptotic behavior for supercritical branching processes," Statistics & Probability Letters, Elsevier, vol. 195(C).
    12. Li, Junping & Meng, Weiwei, 2017. "Regularity criterion for 2-type Markov branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 109-118.
    13. He, Guoman & Zhang, Hanjun & Zhu, Yixia, 2019. "On the quasi-ergodic distribution of absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 116-123.
    14. Ren, Yan-Xia & Song, Renming & Sun, Zhenyao, 2020. "Limit theorems for a class of critical superprocesses with stable branching," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4358-4391.

    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:192:y:2023:i:c:s016771522200205x. 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.