IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs

Listed author(s):
  • Pokern, Y.
  • Stuart, A.M.
  • van Zanten, J.H.
Registered author(s):

    We study a Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data. Rewriting the likelihood in terms of local time of the process, and specifying a Gaussian prior with precision operator of differential form, we show that the posterior is also Gaussian with the precision operator also of differential form. The resulting expressions are explicit and lead to algorithms which are readily implementable. Using new functional limit theorems for the local time of diffusions on the circle, we bound the rate at which the posterior contracts around the true drift function.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 2 ()
    Pages: 603-628

    in new window

    Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:603-628
    DOI: 10.1016/
    Contact details of provider: Web page:

    Order Information: Postal: http://

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    in new window

    1. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
    2. Harry Van Zanten, 2003. "On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 6(2), pages 199-213, May.
    3. Omiros Papaspiliopoulos & Yvo Pokern & Gareth O. Roberts & Andrew M. Stuart, 2012. "Nonparametric estimation of diffusions: a differential equations approach," Biometrika, Biometrika Trust, vol. 99(3), pages 511-531.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:603-628. 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)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.