IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4899-2323-3_13.html
   My bibliography  Save this book chapter

Measure-Theoretic Boundaries of Markov Chains, 0–2 Laws and Entropy

In: Harmonic Analysis and Discrete Potential Theory

Author

Listed:
  • Vadim A. Kaimanovich

    (University of Edinburgh, Department of Mathematics)

Abstract

The classic Poisson formula giving an integral representation of bounded harmonic functions in the unit disk in terms of its boundary values has a long history (as it follows from its very name). Given a Markov operator P on a state space X one can easily define harmonic functions as invariant functions of the operator P, but in order to speak about their boundary values one needs a boundary, because no boundary is normally attached to the state space of a Markov chain (as distinct from bounded Euclidean domains common for the classic potential theory).

Suggested Citation

  • Vadim A. Kaimanovich, 1992. "Measure-Theoretic Boundaries of Markov Chains, 0–2 Laws and Entropy," Springer Books, in: Massimo A. Picardello (ed.), Harmonic Analysis and Discrete Potential Theory, pages 145-180, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2323-3_13
    DOI: 10.1007/978-1-4899-2323-3_13
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-1-4899-2323-3_13. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.