IDEAS home Printed from https://ideas.repec.org/p/ams/ndfwpp/11-03.html
   My bibliography  Save this paper

Phenomenological and ratio bifurcations of a class of discrete time stochastic processes

Author

Listed:
  • Diks, C.G.H.

    (University of Amsterdam)

  • Wagener, F.O.O.

    (University of Amsterdam)

Abstract

Zeeman proposed a classification of stochastic dynamical systems based on the Morse classification of their invariant probability densities; the associated bifurcations are the ‘phenomenological bifurcations’ of L. Arnold. The classification is however not invariant under diffeomorphisms of the state space. In a recent paper we proposed an alternative classification, based on an invariant that is a ratio of joint and marginal probability density functions, that does not suffer from this defect. This classification entails the concept of what we call ‘ratio bifurcations’. In this note it is shown that for a large class of dynamical systems, ratio bifurcations and phenomenological bifurcations actually coincide. Moreover, we link the ratio invariant to the transformation invariant function that Wagenmakers et al. obtained for stochastic differential equations. The results are illustrated with numerical applications to stochastic dynamical systems.

Suggested Citation

  • Diks, C.G.H. & Wagener, F.O.O., 2011. "Phenomenological and ratio bifurcations of a class of discrete time stochastic processes," CeNDEF Working Papers 11-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    • Handle: RePEc:ams:ndfwpp:11-03
    as

    Download full text from publisher

    File URL: http://cendef.uva.nl/binaries/content/assets/subsites/amsterdam-school-of-economics/amsterdam-school-of-economics-research-institute/cendef/working-papers-2011/phenomenon---preprint_diks_wagener.pdf?1363340912226
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Schmitt, Noemi & Westerhoff, Frank, 2017. "On the bimodality of the distribution of the S&P 500's distortion: Empirical evidence and theoretical explanations," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 34-53.
    2. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.

    More about this item

    Statistics

    Access and download statistics

    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:ams:ndfwpp:11-03. 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: Cees C.G. Diks (email available below). General contact details of provider: https://edirc.repec.org/data/cnuvanl.html .

    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.