IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v9y1979i1p35-53.html
   My bibliography  Save this article

The inverse balayage problem for Markov chains, part II

Author

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

Abstract

This paper continues the study of the inverse balayage problem for Markov chains. Let X be a Markov chain with state space A [up curve] B2, let v be a probability measure on B2 and let M(v) consist of probability measures [mu] on A whose X-balayage onto B2 is v. The faces of the compact, convex set M(v) are characterized. For fixed [mu] [epsilon] M(v) the set M([mu],v) of the measures [gimel, Hebrew] of the form [gimel, Hebrew](·) = P[mu]{X(S) [epsilon] ·}, where S is a randomized stopping time, is analyzed in detail. In particular, its extreme points and edge are explicitly identified. A naturally defined reversed chain X, for which v is an inverse balayage of [mu], is introduced and the relation between X and X is studied. The question of which [gimel, Hebrew] [epsilon] M([mu], v) admit a natural stopping time S[gimel, Hebrew] of X (not involving an independent randomization) such that [gimel, Hebrew](·) = P[mu]{X(S[gimel, Hebrew]) [epsilon] ·}, is shown to have rather different answers in discrete and continuous time. Illustrative examples are presented.

Suggested Citation

  • Karr, A. F. & Pittenger, A. O., 1979. "The inverse balayage problem for Markov chains, part II," Stochastic Processes and their Applications, Elsevier, vol. 9(1), pages 35-53, August.
    • Handle: RePEc:eee:spapps:v:9:y:1979:i:1:p:35-53
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(79)90038-3
    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.

    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:9:y:1979:i:1:p:35-53. 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.