IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v238y2026ics0167715226002142.html

From the GNZ identity to a Dyson–Schwinger cumulant hierarchy for point processes

Author

Listed:
  • Clark, Daniel E.

Abstract

The Georgii–Nguyen–Zessin identity induces a functional differential equation for the cumulant generating functional of a point process admitting a Papangelou conditional intensity. In generating-functional form, this equation takes the structure of a Dyson–Schwinger identity. For pairwise Gibbs point processes, the equation closes: insertion of a point acts as a deterministic shift of the source field. This yields a hierarchy for cumulant densities of all orders, expressing cumulants as differences between the original law and the laws induced by point insertion. The formulation is non-perturbative and provides exact recursion relations for cumulants.

Suggested Citation

  • Clark, Daniel E., 2026. "From the GNZ identity to a Dyson–Schwinger cumulant hierarchy for point processes," Statistics & Probability Letters, Elsevier, vol. 238(C).
    • Handle: RePEc:eee:stapro:v:238:y:2026:i:c:s0167715226002142
    DOI: 10.1016/j.spl.2026.110850
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715226002142
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2026.110850?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:stapro:v:238:y:2026:i:c:s0167715226002142. 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/622892/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.