IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v64y1996i2p237-255.html
   My bibliography  Save this article

Fixed lag smoothing of scalar diffusions. Part I. The filtering-smoothing equation

Author

Listed:
  • Liptser, R. Sh.
  • Steinberg, Y.
  • Bobrovsky, B. Z.
  • Schuss, Z.

Abstract

The problem of optimal fixed lag smoothing of a diffusion process, xt is to estimate xt - [tau] for t > [tau], given the output of a nonlinear noisy sensor up to time t. The nonlinear filtering-smoothing problem is to estimate both xt and xt - [tau]. The optimal estimators are the conditional expectations of the processes, given the measurements. We derive evolution equations for both the normalized and unnormalized versions of the joint probability density function of xt and xt - [tau], given the noisy measurements. The former is an equation of Kushner's type and the latter is of Zakai's type.

Suggested Citation

  • Liptser, R. Sh. & Steinberg, Y. & Bobrovsky, B. Z. & Schuss, Z., 1996. "Fixed lag smoothing of scalar diffusions. Part I. The filtering-smoothing equation," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 237-255, November.
    • Handle: RePEc:eee:spapps:v:64:y:1996:i:2:p:237-255
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(96)00086-5
    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. van Kampen, N.G., 1997. "Noise in the current through a membrane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 244(1), pages 414-425.

    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:64:y:1996:i:2:p:237-255. 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.