IDEAS home Printed from
   My bibliography  Save this article

An optimal control variance reduction method for density estimation


  • Kebaier, Ahmed
  • Kohatsu-Higa, Arturo


We study the problem of density estimation of a non-degenerate diffusion using kernel functions. Thanks to Malliavin calculus techniques, we obtain an expansion of the discretization error. Then, we introduce a new control variate method in order to reduce the variance in the density estimation. We prove a stable law convergence theorem of the type obtained in Jacod-Kurtz-Protter for the first Malliavin derivative of the error process, which leads us to get a CLT for the new control variate algorithm. This CLT gives us a precise description of the optimal parameters of the method.

Suggested Citation

  • Kebaier, Ahmed & Kohatsu-Higa, Arturo, 2008. "An optimal control variance reduction method for density estimation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2143-2180, December.
  • Handle: RePEc:eee:spapps:v:118:y:2008:i:12:p:2143-2180

    Download full text from publisher

    File URL:
    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.

    References listed on IDEAS

    1. Arturo Kohatsu & Roger Pettersson, 2002. "Variance reduction methods for simulation of densities on Wiener space," Economics Working Papers 597, Department of Economics and Business, Universitat Pompeu Fabra.
    2. BALLY Vlad & TALAY Denis, 1996. "The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density," Monte Carlo Methods and Applications, De Gruyter, vol. 2(2), pages 93-128, December.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Delong, Lukasz & Imkeller, Peter, 2010. "On Malliavin's differentiability of BSDEs with time delayed generators driven by Brownian motions and Poisson random measures," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1748-1775, August.


    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:118:y:2008:i:12:p:2143-2180. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.