IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v172y2024ics0304414924000413.html
   My bibliography  Save this article

A geometric extension of the Itô-Wentzell and Kunita’s formulas

Author

Listed:
  • Bethencourt de León, Aythami
  • Takao, So

Abstract

We extend the Itô-Wentzell formula for the evolution along a continuous semimartingale of a time-dependent stochastic field driven by a continuous semimartingale to tensor field-valued stochastic processes on manifolds. More concretely, we investigate how the pull-back (respectively, the push-forward) by a stochastic flow of diffeomorphisms of a time-dependent stochastic tensor field driven by a continuous semimartingale evolves with time, deriving it under suitable regularity conditions. We call this result the Kunita-Itô-Wentzell (KIW) formula for the advection of tensor-valued stochastic processes. Equations of this nature bear significance in stochastic fluid dynamics and well-posedness by noise problems, facilitating the development of certain geometric extensions within existing theories.

Suggested Citation

  • Bethencourt de León, Aythami & Takao, So, 2024. "A geometric extension of the Itô-Wentzell and Kunita’s formulas," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:spapps:v:172:y:2024:i:c:s0304414924000413
    DOI: 10.1016/j.spa.2024.104335
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924000413
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104335?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:172:y:2024:i:c:s0304414924000413. 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.