IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v38y2025i1d10.1007_s10959-024-01397-3.html
   My bibliography  Save this article

Propagation of Chaos for Point Processes Induced by Particle Systems with Mean-Field Drift Interaction

Author

Listed:
  • Nikolaos Kolliopoulos

    (University of Michigan)

  • Martin Larsson

    (Carnegie Mellon University)

  • Zeyu Zhang

    (Carnegie Mellon University)

Abstract

We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: It has the same weak limit as the point process induced by i.i.d. copies of the solution of a limiting McKean–Vlasov equation. This weak limit is a Poisson point process whose intensity measure is related to classical extreme value distributions. In particular, this yields the limiting distribution of the normalized upper order statistics.

Suggested Citation

  • Nikolaos Kolliopoulos & Martin Larsson & Zeyu Zhang, 2025. "Propagation of Chaos for Point Processes Induced by Particle Systems with Mean-Field Drift Interaction," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-22, March.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01397-3
    DOI: 10.1007/s10959-024-01397-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-024-01397-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-024-01397-3?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.

    References listed on IDEAS

    as
    1. Anastasia Borovykh & Andrea Pascucci & Stefano La Rovere, 2018. "Systemic risk in a mean-field model of interbank lending with self-exciting shocks," IISE Transactions, Taylor & Francis Journals, vol. 50(9), pages 806-819, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    2. Morteza Alaeddini & Philippe Madiès & Paul J. Reaidy & Julie Dugdale, 2023. "Interbank money market concerns and actors’ strategies—A systematic review of 21st century literature," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 573-654, April.
    3. Yaguang Wu & Qingan Qiu, 2022. "Optimal Triggering Policy of Protective Devices Considering Self-Exciting Mechanism of Shocks," Mathematics, MDPI, vol. 10(15), pages 1-18, August.
    4. Chotipong Charoensom & Thaisiri Watewai, 2022. "Optimal Liquidity Control and Systemic Risk in an Interbank Network with Liquidity Shocks and Regime-dependent Interconnectedness," PIER Discussion Papers 175, Puey Ungphakorn Institute for Economic Research.
    5. Zachary Feinstein & Andreas Sojmark, 2019. "A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field," Papers 1912.08695, arXiv.org.

    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:spr:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01397-3. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.