IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v176y2024ics0304414924001388.html
   My bibliography  Save this article

Sample path moderate deviations for shot noise processes in the high intensity regime

Author

Listed:
  • Anugu, Sumith Reddy
  • Pang, Guodong

Abstract

We study the sample-path moderate deviation principle (MDP) for shot noise processes in the high intensity regime. The shot noise processes have a renewal arrival process, non-stationary noises (with arrival-time dependent distributions) and a general shot response function of the noises. The rate function in the MDP exhibits a memory phenomenon in this asymptotic regime, which is in contrast with that in the conventional time–space scaling regime. To prove the sample-path MDP, we first establish that this is equivalent to establishing the sample-path MDP of another process that is easier to study. We prove its finite-dimensional MDP and then establish the exponential tightness under the Skorohod J1 topology. This results in the sample-path MDP in D under the Skorohod J1 topology with a rate function that is derived from the rate function in the finite-dimensional MDP using the tools of reproducing kernel Hilbert space. In the proofs, because of the non-stationarity of shot noise process, we establish a new exponential maximal inequality and use it to prove exponential tightness and the aforementioned equivalence.

Suggested Citation

  • Anugu, Sumith Reddy & Pang, Guodong, 2024. "Sample path moderate deviations for shot noise processes in the high intensity regime," Stochastic Processes and their Applications, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:spapps:v:176:y:2024:i:c:s0304414924001388
    DOI: 10.1016/j.spa.2024.104432
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924001388
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104432?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.

    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:spapps:v:176:y:2024:i:c:s0304414924001388. 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/505572/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.