IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v225y1996i1p62-80.html
   My bibliography  Save this article

On the low-dimensional modelling of Stratonovich stochastic differential equations

Author

Listed:
  • Xu, Chao
  • Roberts, A.J.

Abstract

We develop further ideas on how to construct low-dimensional models of stochastic dynamical systems. The aim is to derive a consistent and accurate model from the originally high-dimensional system. This is done with the support of centre manifold theory and techniques. Aspects of several previous approaches are combined and extended: adiabatic elimination has previously been used, but centre manifold techniques simplify the noise by removing memory effects, and with less algebraic effort than normal forms; analysis of associated Fokker-Plank equations replace nonlinearly generated noise processes by their long-term equivalent white noise. The ideas are developed by examining a simple dynamical system which serves as a prototype of more interesting physical situations.

Suggested Citation

  • Xu, Chao & Roberts, A.J., 1996. "On the low-dimensional modelling of Stratonovich stochastic differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 225(1), pages 62-80.
    • Handle: RePEc:eee:phsmap:v:225:y:1996:i:1:p:62-80
    DOI: 10.1016/0378-4371(95)00387-8
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437195003878
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(95)00387-8?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. Bunder, J.E. & Roberts, A.J., 2017. "Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 164-179.
    2. Roberts, A.J., 2008. "Normal form transforms separate slow and fast modes in stochastic dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 12-38.

    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:phsmap:v:225:y:1996:i:1:p:62-80. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.