IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v129y2019i2p355-380.html
   My bibliography  Save this article

MEXIT: Maximal un-coupling times for stochastic processes

Author

Listed:
  • Ernst, Philip A.
  • Kendall, Wilfrid S.
  • Roberts, Gareth O.
  • Rosenthal, Jeffrey S.

Abstract

Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts.

Suggested Citation

  • Ernst, Philip A. & Kendall, Wilfrid S. & Roberts, Gareth O. & Rosenthal, Jeffrey S., 2019. "MEXIT: Maximal un-coupling times for stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 355-380.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:2:p:355-380
    DOI: 10.1016/j.spa.2018.03.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918300425
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2018.03.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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:129:y:2019:i:2:p:355-380. 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.