IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i8p1393-1401.html
   My bibliography  Save this article

Interplay between positive feedbacks in the generalized CEV process

Author

Listed:
  • Reimann, St.
  • Gontis, V.
  • Alaburda, M.

Abstract

The dynamics of the generalized CEV process dXt=aXtndt+bXtmdWt(gCEV) is due to an interplay of two feedback mechanisms: State-to-Drift and State-to-Diffusion, whose degrees are n and m respectively. We particularly show that the gCEV, in which both feedback mechanisms are positive, i.e. n,m>1, admits a stationary probability distribution P provided that n<2m−1. In this case the stationary pdf asymptotically decays as a power law P(x)∼1xμ with tail exponent μ=2m>2. Furthermore the power spectral density obeys S(f)∼1fβ, where β=2−1+ϵ2(m−1), ϵ>0. The tail behavior of the stationary pdf as well as of the power-spectral density thus are both independent of the drift feedback degree n but governed by the diffusion feedback degree m. Bursting behavior of the gCEV is investigated numerically. Burst intensity S and burst duration T are shown to be related by S∼T2.

Suggested Citation

  • Reimann, St. & Gontis, V. & Alaburda, M., 2011. "Interplay between positive feedbacks in the generalized CEV process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(8), pages 1393-1401.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:8:p:1393-1401
    DOI: 10.1016/j.physa.2010.11.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110010071
    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/j.physa.2010.11.043?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. Kononovicius, A. & Gontis, V., 2012. "Agent based reasoning for the non-linear stochastic models of long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1309-1314.
    2. Vygintas Gontis & Aleksejus Kononovicius & Stefan Reimann, 2012. "The class of nonlinear stochastic models as a background for the bursty behavior in financial markets," Papers 1201.3083, arXiv.org, revised May 2012.

    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:390:y:2011:i:8:p:1393-1401. 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.