IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v8y1978i2p199-209.html
   My bibliography  Save this article

The limiting distribution for the infinitely deep dam with a Markovian input

Author

Listed:
  • Pakes, Anthony G.
  • Phatarfod, R. M.

Abstract

The paper outlines a case for taking greater interest in the bottomless, or infinitely deep, dam model in Hydrology. It then shows that for such a model with unit withdrawals and an ergodic Markov chain input process the limiting distribution of depletion, when this exists, is a zero modified geometric distribution. This result generalises the well known result for independent inputs. The technical conditions required for the proof are satisfied for finite state space input processes and are shown to be satisfied by certain infinite state space input processes. These include as special cases examples which have a negative binomial limiting input distribution.

Suggested Citation

  • Pakes, Anthony G. & Phatarfod, R. M., 1978. "The limiting distribution for the infinitely deep dam with a Markovian input," Stochastic Processes and their Applications, Elsevier, vol. 8(2), pages 199-209, December.
  • Handle: RePEc:eee:spapps:v:8:y:1978:i:2:p:199-209
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(78)90008-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.

    Citations

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


    Cited by:

    1. Bruneel, Herwig & Maertens, Tom & Walraevens, Joris, 2014. "Class clustering destroys delay differentiation in priority queues," European Journal of Operational Research, Elsevier, vol. 235(1), pages 149-158.

    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:8:y:1978:i:2:p:199-209. 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.