IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v39y1991i2p287-299.html
   My bibliography  Save this article

The joint distribution of sojourn times in finite semi-Markov processes

Author

Listed:
  • Csenki, Attila

Abstract

Let Y={Yt:t[greater-or-equal, slanted]0} be a semi-Markov process whose state space S is finite. Assume that Y is either irreducible and S is then partitioned into two classes A1, A2, or that Y is absorbing and S is partitioned into A1, A2, A3, where A3 is the set of all absorbing states of Y. Denoting by TAi,j the jth sojourn of Y in Ai, i=1, 2, we determine the Laplace transform of the joint distribution of T={TAi,j:i=1, 2; J=1,..., m}. This result is derived from a recurrence relation for the Laplace transform of T. The proof of the recurrence relation itself is based on what could be called a 'generalized renewal argument'. Some known results on sojourn times in Markov and semi-Markov processes are also rederived using our main theorem. A procedure for obtaining the Laplace transform of the vector of sojourn times in special cases if S is partitioned into more than two non-absorbing classes is also considered.

Suggested Citation

  • Csenki, Attila, 1991. "The joint distribution of sojourn times in finite semi-Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 39(2), pages 287-299, December.
    • Handle: RePEc:eee:spapps:v:39:y:1991:i:2:p:287-299
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(91)90084-P
    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. Yi, He & Cui, Lirong, 2017. "Distribution and availability for aggregated second-order semi-Markov ternary system with working time omission," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 50-60.

    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:39:y:1991:i:2:p:287-299. 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.