IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v23y1975i6p1143-1154.html
   My bibliography  Save this article

Application of a Functional Equation to a Class of Stochastic Detection Models

Author

Listed:
  • Barry Belkin

    (Daniel H. Wagner, Associates, Paoli, Pennsylvania)

Abstract

In a proposed class of abstract stochastic detection models, the occurrence of detection is related to the time-dependent behavior of a detection functional defined on the signal-to-noise process sample paths. We describe a potential operations-analysis application in certain sonar detection problems. The method developed for computing detection probabilities for these models requires the solution of a functional equation involving the detection functional and the weak infinitesimal operator of the signal-to-noise process, assumed Markovian with stationary transition probabilities. Two hypothetical signal-to-noise processes considered in detail are the random sampling process and the stationary Gauss-Markov (Ornstein-Uhlenbeck) process in the special case when the detection functional measures time above a constant threshold level. We compare expressions for the mean time to detect, obtained for these processes, numerically.

Suggested Citation

  • Barry Belkin, 1975. "Application of a Functional Equation to a Class of Stochastic Detection Models," Operations Research, INFORMS, vol. 23(6), pages 1143-1154, December.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:6:p:1143-1154
    DOI: 10.1287/opre.23.6.1143
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.23.6.1143
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.23.6.1143?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
    ---><---

    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:inm:oropre:v:23:y:1975:i:6:p:1143-1154. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.