IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p881-d1062910.html
   My bibliography  Save this article

Exponential Inequality of Marked Point Processes

Author

Listed:
  • Chen Li

    (Institute for Financial Studies, Shandong University, Jinan 250100, China)

  • Yuping Song

    (School of Finance and Business, Shanghai Normal University, Shanghai 200234, China)

Abstract

This paper presents the uniform concentration inequality for the stochastic integral of marked point processes. We developed a new chaining method to obtain the results. Our main result is presented under an entropy condition for partitioning the index set of the integrands. Our result is an improvement of the work of van de Geer on exponential inequalities for martingales in 1995. As applications of the main result, we also obtained the uniform concentration inequality of functional indexed empirical processes and the Kakutani–Hellinger distance of the maximum likelihood estimator.

Suggested Citation

  • Chen Li & Yuping Song, 2023. "Exponential Inequality of Marked Point Processes," Mathematics, MDPI, vol. 11(4), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:881-:d:1062910
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/881/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/881/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wang, Hanchao & Lin, Zhengyan & Su, Zhonggen, 2019. "On Bernstein type inequalities for stochastic integrals of multivariate point processes," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1605-1621.
    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. Naiqi Liu & Vladimir V. Ulyanov & Hanchao Wang, 2022. "On De la Peña Type Inequalities for Point Processes," Mathematics, MDPI, vol. 10(12), pages 1-13, June.

    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:11:y:2023:i:4:p:881-:d:1062910. 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: 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.