IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v51y1994i1p1-7.html
   My bibliography  Save this article

Autoregressive approximation in branching processes with a threshold

Author

Listed:
  • Klebaner, F. C.
  • Nerman, O.

Abstract

It is shown that population dependent branching processes for large values of threshold can be approximated by Gaussian processes centered at the iterates of the corresponding deterministic function. If the deterministic system has a stable limit cycle, then in the vicinity of the cycle points the corresponding stochastic system can be approximated by an autoregressive process. It is shown that it is possible to speed up convergence to the limit so that the processes converge weakly to the stationary autoregressive process. Similar results hold for noisy dynamical systems when random noise satisfies certain conditions and the corresponding dynamical system has stable limit cycles.

Suggested Citation

  • Klebaner, F. C. & Nerman, O., 1994. "Autoregressive approximation in branching processes with a threshold," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 1-7, June.
    • Handle: RePEc:eee:spapps:v:51:y:1994:i:1:p:1-7
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(93)00000-6
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ramanan, Kavita & Zeitouni, Ofer, 1999. "The quasi-stationary distribution for small random perturbations of certain one-dimensional maps," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 25-51, November.
    2. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.
    3. Klebaner, F. C. & Liptser, R., 1999. "Moderate deviations for randomly perturbed dynamical systems," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 157-176, April.
    4. Högnäs, Göran, 1997. "On the quasi-stationary distribution of a stochastic Ricker model," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 243-263, October.
    5. Christine Jacob, 2010. "Branching Processes: Their Role in Epidemiology," IJERPH, MDPI, vol. 7(3), pages 1-19, March.

    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:51:y:1994:i:1:p:1-7. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.