IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i2p284-d1569038.html
   My bibliography  Save this article

Controlled Filtered Poisson Processes

Author

Listed:
  • Mario Lefebvre

    (Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-Ville, Montréal, QC H3C 3A7, Canada)

Abstract

Filtered Poisson processes are used as models in various applications, in particular in statistical hydrology. In this paper, controlled filtered Poisson processes are considered. The aim is to minimize the expected time that the process will spend in the continuation region. The dynamic programming equation satisfied by the value function is derived. To obtain the value function, and hence the optimal control, a non-linear integro-differential equation must be solved, subject to the appropriate boundary conditions. Various cases for the size of the jumps are treated and explicit results are obtained.

Suggested Citation

  • Mario Lefebvre, 2025. "Controlled Filtered Poisson Processes," Mathematics, MDPI, vol. 13(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:284-:d:1569038
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/2/284/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/2/284/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:13:y:2025:i:2:p:284-:d:1569038. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.