IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v28y2015i3d10.1007_s10959-013-0533-9.html
   My bibliography  Save this article

Stochastic Averaging for a Hamiltonian System with Skew Random Perturbations

Author

Listed:
  • Chetan D. Pahlajani

    (University of Delaware)

Abstract

We consider a stochastic process that arises due to small random perturbations of a particle moving along the orbits of a double-well Hamiltonian. The perturbing noise is assumed to have skewness along the infinity-shaped homoclinic orbit of the Hamiltonian. As the noise strength goes to zero, we characterize the limiting dynamics in terms of a graph-valued Markov process. The effort centers around the construction of certain perturbed test functions needed to prove convergence. Following Sowers, we accomplish this through the development of suitable corrector functions in a boundary layer near the homoclinic orbit.

Suggested Citation

  • Chetan D. Pahlajani, 2015. "Stochastic Averaging for a Hamiltonian System with Skew Random Perturbations," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1165-1226, September.
    • Handle: RePEc:spr:jotpro:v:28:y:2015:i:3:d:10.1007_s10959-013-0533-9
    DOI: 10.1007/s10959-013-0533-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-013-0533-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-013-0533-9?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.

    References listed on IDEAS

    as
    1. Freidlin, M. I. & Wentzell, A. D., 2004. "Diffusion processes on an open book and the averaging principle," Stochastic Processes and their Applications, Elsevier, vol. 113(1), pages 101-126, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Wujun Lv & Xing Huang, 2021. "Harnack and Shift Harnack Inequalities for Degenerate (Functional) Stochastic Partial Differential Equations with Singular Drifts," Journal of Theoretical Probability, Springer, vol. 34(2), pages 827-851, June.

    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. Zsolt Pajor-Gyulai & Michael Salins, 2016. "On Dynamical Systems Perturbed by a Null-Recurrent Fast Motion: The Continuous Coefficient Case with Independent Driving Noises," Journal of Theoretical Probability, Springer, vol. 29(3), pages 1083-1099, September.

    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:spr:jotpro:v:28:y:2015:i:3:d:10.1007_s10959-013-0533-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.