IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v56y1995i1p133-149.html
   My bibliography  Save this article

Sur l'approximation de la distribution stationnaire d'une chaîne de Markov stochastiquement monotone

Author

Listed:
  • Simonot, F.

Abstract

Let P be an infinite irreducible stochastic matrix, stochastically dominated by an irreducible, positive-recurrent and stochastically monotone stochastic matrix Q. Let Pn be any n x n stochastic matrix with Pn [greater-or-equal, slanted] Tn, where Tn denotes the n x n northwest corner truncation of P. We first show that these assumptions imply the existence of limiting distributions [mu], [pi], [pi]n for Q, P, Pn respectively; moreover, if Q obeys a Foster-Lyapounov condition, we derive the rate of convergence of [pi]n to [pi]; as an application of the preceding results, we deal with the random walk on a half line, and prove under mild assumptions that the rate of convergence of [pi]n to [pi] is geometric.

Suggested Citation

  • Simonot, F., 1995. "Sur l'approximation de la distribution stationnaire d'une chaîne de Markov stochastiquement monotone," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 133-149, March.
  • Handle: RePEc:eee:spapps:v:56:y:1995:i:1:p:133-149
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)00062-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Gibson, Diana & Seneta, E., 1987. "Monotone infinite stochastic matrices and their augmented truncations," Stochastic Processes and their Applications, Elsevier, vol. 24(2), pages 287-292, May.
    2. Nico M. van Dijk, 1991. "Truncation of Markov Chains with Applications to Queueing," Operations Research, INFORMS, vol. 39(6), pages 1018-1026, 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. Badredine Issaadi, 2020. "Weak stability bounds for approximations of invariant measures with applications to queueing," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 371-400, March.
    2. Liu, Jinpeng & Liu, Yuanyuan & Zhao, Yiqiang Q., 2022. "Augmented truncation approximations to the solution of Poisson’s equation for Markov chains," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    3. van Dijk, Nico M., 2008. "Error bounds for state space truncation of finite Jackson networks," European Journal of Operational Research, Elsevier, vol. 186(1), pages 164-181, April.
    4. Braunsteins, Peter & Decrouez, Geoffrey & Hautphenne, Sophie, 2019. "A pathwise approach to the extinction of branching processes with countably many types," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 713-739.
    5. Cruz, Juan Alberto Rojas, 2020. "Sensitivity of the stationary distributions of denumerable Markov chains," Statistics & Probability Letters, Elsevier, vol. 166(C).
    6. Yiqiang Q. Zhao & W. John Braun & Wei Li, 1999. "Northwest corner and banded matrix approximations to a Markov chain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(2), pages 187-197, March.
    7. Jianyu Cao & Weixin Xie, 2017. "Stability of a two-queue cyclic polling system with BMAPs under gated service and state-dependent time-limited service disciplines," Queueing Systems: Theory and Applications, Springer, vol. 85(1), pages 117-147, February.

    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:spapps:v:56:y:1995:i:1:p:133-149. 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/505572/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.