IDEAS home Printed from
   My bibliography  Save this article

Characterization of Multivariate Stationary Gaussian Reciprocal Diffusions,


  • Lévy, Bernard C.


Jamison's classification of scalar stationary Gaussian reciprocal processes is extended to multivariate Gaussian reciprocal diffusions (GRDs). The second-order self-adjoint differential equation satisfied by the covariance of a GRD specifies a Hamiltonian matrix whose eigenstructure is employed to parametrize the covariance of stationary GRDs. Characterizations of the conservation matrix and of the covariance matrix of the end point values of a stationary GRD are also provided.

Suggested Citation

  • Lévy, Bernard C., 1997. "Characterization of Multivariate Stationary Gaussian Reciprocal Diffusions, ," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 74-99, July.
  • Handle: RePEc:eee:jmvana:v:62:y:1997:i:1:p:74-99

    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. Recoules, Raymond, 1991. "Gaussian reciprocal processes revisited," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 297-303, October.
    2. Carmichael, J.P. & Masse´, J.C. & Theodorescu, R., 1987. "Multivariate reciprocal stationary Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 47-66, October.
    3. Carmichael, J. -P. & Massé, J. -C. & Theodorescu, R., 1991. "Reciprocal covariance solutions of some matrix differential equations," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 45-60, February.
    4. Chay, S. C., 1972. "On quasi-Markov random fields," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 14-76, March.
    Full references (including those not matched with items on IDEAS)


    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:jmvana:v:62:y:1997:i:1:p:74-99. 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.