IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v178y2024ics0304414924001844.html
   My bibliography  Save this article

Large deviations for slow–fast processes on connected complete Riemannian manifolds

Author

Listed:
  • Hu, Yanyan
  • Kraaij, Richard C.
  • Xi, Fubao

Abstract

We consider a class of slow–fast processes on a connected complete Riemannian manifold M. The limiting dynamics as the scale separation goes to ∞ is governed by the averaging principle. Around this limit, we prove large deviation principles with an action-integral rate function for the slow process by nonlinear semigroup methods together with Hamilton–Jacobi–Bellman (HJB) equation techniques. Our main innovation is solving the comparison principle for viscosity solutions for the HJB equation on M and the construction of a variational viscosity solution for the non-smooth Hamiltonian, which lies at the heart of deriving the action integral representation for the rate function.

Suggested Citation

  • Hu, Yanyan & Kraaij, Richard C. & Xi, Fubao, 2024. "Large deviations for slow–fast processes on connected complete Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:spapps:v:178:y:2024:i:c:s0304414924001844
    DOI: 10.1016/j.spa.2024.104478
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924001844
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104478?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:178:y:2024:i:c:s0304414924001844. 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.