IDEAS home Printed from https://ideas.repec.org/p/bep/unimip/unimi-1016.html
   My bibliography  Save this paper

IFSM representation of Brownian motion with applications to simulation

Author

Listed:
  • Stefano Iacus

    (Department of Economics, Business and Statistics, University of Milan, IT)

  • Davide La Torre

    (Department of Economics, Business and Statistics, University of Milan, IT)

Abstract

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L^2 decomposition like the Kac-Siegert/Karnounen-Loeve series. In this paper we first propose a IFSM (Iterated Function Systems with Maps) operator whose fixed point is the trajectory of the BM. We then use this representation of the process to simulate its trajectories. The resulting simulated trajectories are self-affine, continuous and fractal by construction. This fact produces more realistic trajectories than other schemes in the sense that their geometry is closer to the one of the true BM's trajectories. The IFSM trajectory of the BM can then be used to generate more realistic solutions of stochastic differential equations.

Suggested Citation

  • Stefano Iacus & Davide La Torre, 2006. "IFSM representation of Brownian motion with applications to simulation," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1016, Universitá degli Studi di Milano.
    • Handle: RePEc:bep:unimip:unimi-1016
    Note: oai:cdlib1:unimi-1016
    as

    Download full text from publisher

    File URL: http://services.bepress.com/unimi/statistics/art6
    Download Restriction: no
    ---><---

    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:bep:unimip:unimi-1016. 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: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/damilit.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.