IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v60y1995i2p287-311.html
   My bibliography  Save this article

On the exit law from saddle points

Author

Listed:
  • Day, Martin V.

Abstract

We consider the effects of adding an asymptotically small random (Brownian) perturbation to a planar dynamical system with a saddle point equilibrium. By applying techniques developed for the problem of exit from a stable equilibrium, we obtain a new limit law for the exit time from a neighborhood of the saddle, assuming the initial point is on the stable manifold. The limit law shows that the exit distribution depends on (the logarithm of) the noise parameter in an additive way. This gives a more accurate description of the exit law than the previous (but more general) results of Kifer and Mikami. Generalization to higher dimensions seems likely, although only if the unstable manifold has dimension 1.

Suggested Citation

  • Day, Martin V., 1995. "On the exit law from saddle points," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 287-311, December.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:2:p:287-311
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(95)00063-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Almada Monter, Sergio Angel, 2015. "Quadratic covariation estimates in non-smooth stochastic calculus," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 343-361.

    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:60:y:1995:i:2:p:287-311. 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.