IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/200190.html
   My bibliography  Save this paper

On Itô's formula for multidimensional Brownian motion

Author

Listed:
  • Föllmer, Hans
  • Protter, Philip E.

Abstract

Consider a d-dimensional Brownian motion X (Xl, ... ,Xd ) and a function F which belongs locally to the Sobolev space W 1,2. We prove an extension of Ito's formula where the usual second order terms are replaced by the quadratic covariations [fk(X), Xkj involving the weak first partial derivatives fk of F. In particular we show that for any locally square-integrable function f the quadratic covariations [f(X), Xkj exist as limits in probability for any starting point, except for some polar set. The proof is based on new approximation results for forward and backward stochastic integrals.

Suggested Citation

  • Föllmer, Hans & Protter, Philip E., 2001. "On Itô's formula for multidimensional Brownian motion," SFB 373 Discussion Papers 2001,90, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200190
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/62732/1/725954108.pdf
    Download Restriction: no

    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:zbw:sfb373:200190. 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: (ZBW - German National Library of Economics). General contact details of provider: http://edirc.repec.org/data/sfhubde.html .

    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 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.

    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.