IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v32y1989i1p3-45.html
   My bibliography  Save this article

Filtered statistical models and Hellinger processes

Author

Listed:
  • Jacod, Jean

Abstract

In this paper we extend the notion of Hellinger processes, which was known for pairs of probability measures defined on a filtered space, to general filtered statistical experiments. In a sense, this notion generalizes the Mellin transforms of a (nonfiltered) statistical experiment. Then we characterize several properties of statistical experiments in terms of their Hellinger processes, namely the continuity of the likelihood processes, or the property that the likelihood processes are exponentials of processes with independent increments, or the Gaussian property of likelihoods. We also devote a lot of space to proving that, under mild additional assumptions, a statistical model is "generated" by a process with independent increments if and only if it has deterministic Hellinger processes.

Suggested Citation

  • Jacod, Jean, 1989. "Filtered statistical models and Hellinger processes," Stochastic Processes and their Applications, Elsevier, vol. 32(1), pages 3-45, June.
    • Handle: RePEc:eee:spapps:v:32:y:1989:i:1:p:3-45
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(89)90052-5
    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.

    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:32:y:1989:i:1:p:3-45. 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.