IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space

  • Tweedie, Richard L.
Registered author(s):

    Let {Xn} be a [empty set][combining character]-irreducible Markov chain on an arbitrary space. Sufficient conditions are given under which the chain is ergodic or recurrent. These extend known results for chains on a countable state space. In particular, it is shown that if the space is a normed topological space, then under some continuity conditions on the transition probabilities of {Xn} the conditions for ergodicity will be met if there is a compact set K and an [epsilon] > 0 such that E {||Xn+1|| -- ||Xn|| | Xn = x} [less-than-or-equals, slant] -[epsilon] whenever x lies outside K and E{||Xn+1|| | Xn=x} is bounded, x [set membership, variant] K; whilst the conditions for recurrence will be met if there exists a compact K with E {||Xn+1|| - ||Xn|| | Xn = x} [less-than-or-equals, slant] 0 for all x outside K. An application to queueing theory is given.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.sciencedirect.com/science/article/B6V1B-45JC7BH-W/2/bf7c82ca88a4e9b4d2e0da14e59db5ac
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 3 (1975)
    Issue (Month): 4 (October)
    Pages: 385-403

    as
    in new window

    Handle: RePEc:eee:spapps:v:3:y:1975:i:4:p:385-403
    Contact details of provider: Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description

    Order Information: Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/OOC/InitController?id=505572&ref=505572_01_ooc_1&version=01

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:3:y:1975:i:4:p:385-403. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.