IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v45y1993i2p309-318.html
   My bibliography  Save this article

Integration of covariance kernels and stationarity

Author

Listed:
  • Lasinger, Rudolf

Abstract

The necessary and sufficient matrix condition of Mitchell, Morris and Ylvisaker (1990) for a stationary Gaussian process to have a specified process as kth derivative is investigated. The mean-square smoothing approach of stationary processes requires integration of covariance functions preserving stationarity. By providing a recursive representation of the involved reproducing kernel Hilbert spaces it is possible to analyse another criterion for k-fold integration of a process. This criterion only contains inequalities for the variances of the integrated processes. If the Hilbert space associated with the covariance function has a special form, which often occurs, then it can be shown that such processes can be integrated arbitrarily often. This is especially the case for the Ornstein-Uhlenbeck process. The results are applied to the linear and the exponential kernel and yield explicit norms in the corresponding reproducing kernel Hilbert spaces for each integration.

Suggested Citation

  • Lasinger, Rudolf, 1993. "Integration of covariance kernels and stationarity," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 309-318, April.
    • Handle: RePEc:eee:spapps:v:45:y:1993:i:2:p:309-318
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(93)90077-H
    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.

    Citations

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


    Cited by:

    1. Blanke, Delphine & Vial, Céline, 2008. "Assessing the number of mean square derivatives of a Gaussian process," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1852-1869, October.

    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:spapps:v:45:y:1993:i:2:p:309-318. 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.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.