IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v31y1989i1p40-58.html
   My bibliography  Save this article

Ito stochastic integral in the dual of a nuclear space

Author

Listed:
  • Bojdecki, Tomasz
  • Jakubowski, Jacek

Abstract

Ito's definition of the stochastic integral with respect to a Wiener process in the dual of a nuclear space is simplified and slightly generalized. This definition yields a completely intrinsic description of the class of random, operator-valued integrands. For a large class of spaces (e.g. for Schwartz distribution spaces) any time-inhomogeneous Wiener process is proved to have a representation as the stochastic integral with respect to a homogeneous (standard) Wiener process. A relation between this definition of stochastic integral and the notion of isometric integral in Hilbert spaces, defined by Metivier, is established.

Suggested Citation

  • Bojdecki, Tomasz & Jakubowski, Jacek, 1989. "Ito stochastic integral in the dual of a nuclear space," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 40-58, October.
    • Handle: RePEc:eee:jmvana:v:31:y:1989:i:1:p:40-58
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(89)90048-1
    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. Bojdecki, Tomasz & Gorostiza, Luis G., 1995. "Self-intersection local time for Gaussian '(d)-processes: Existence, path continuity and examples," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 191-226, December.
    2. Peszat, Szymon & Zabczyk, Jerzy, 1997. "Stochastic evolution equations with a spatially homogeneous Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 187-204, December.

    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:jmvana:v:31:y:1989:i:1:p:40-58. 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/622892/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.