IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v7y1978i2p165-178.html
   My bibliography  Save this article

The inverse balayage problem for Markov chains

Author

Listed:
  • Karr, A. F.
  • Pittenger, A. O.

Abstract

Let X be a Markov chain, let A be a finite sunset of its countable state space. let [small schwa]A consist of states in A' that can be reached in one step from A and let v be a prescribed probability measure on [not partial differential]A. In this paper we study the following inverse exit problem: describe and analyze the set M(v) of probability measures [mu] on A such that P[mu] {X(T)[epsilon]·}=v(·) where T= inl{k: X(k)[epsilon] A'} is the first exit time from A. Characterizations are provided for elements of M(v), extreme points of M(v) and those measures in M(v) that are maximal with respect to a partial ordering induced by excessive functions. Potential theoretic aspects of the problem and one-dimensional birth and death processes are treated in detail, and examples are given that illustrate implications and limitations of the theory.

Suggested Citation

  • Karr, A. F. & Pittenger, A. O., 1978. "The inverse balayage problem for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 7(2), pages 165-178, June.
    • Handle: RePEc:eee:spapps:v:7:y:1978:i:2:p:165-178
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(78)90015-7
    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.

    More about this item

    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:eee:spapps:v:7:y:1978:i:2:p:165-178. 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.