IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v128y2018i7p2367-2403.html
   My bibliography  Save this article

Homogenization of dissipative, noisy, Hamiltonian dynamics

Author

Listed:
  • Birrell, Jeremiah
  • Wehr, Jan

Abstract

We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a noise-induced drift term. We prove convergence to the solution of the homogenized equation in probability and, under stronger assumptions, in an Lp-norm. Applications cover the overdamped limit of particle motion in a time-dependent electromagnetic field, on a manifold with time-dependent metric, and the dynamics of nuclear matter.

Suggested Citation

  • Birrell, Jeremiah & Wehr, Jan, 2018. "Homogenization of dissipative, noisy, Hamiltonian dynamics," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2367-2403.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:7:p:2367-2403
    DOI: 10.1016/j.spa.2017.09.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414917302247
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2017.09.005?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xie, Longjie & Yang, Li, 2022. "The Smoluchowski–Kramers limits of stochastic differential equations with irregular coefficients," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 91-115.

    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:128:y:2018:i:7:p:2367-2403. 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.