EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Issue ESAIM: PS
Volume 12
Page(s) 387 - 411
DOI 10.1051/ps:2007040
Published online 25 July 2008

ESAIM: PS, July 2008, Vol. 12, p. 387-411
DOI: 10.1051/ps:2007040

Stochastic differential equations driven by processes generated by divergence form operators II: convergence results

Antoine Lejay

Projet TOSCA, INRIA & Institut Élie Cartan UMR 7502, Nancy-Université, CNRS, INRIA. Campus scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex, France; Antoine.Lejay@iecn.u-nancy.fr


Received September 12, 2007. Published online 25 July 2008

Abstract
We have seen in a previous article how the theory of "rough paths" allows us to construct solutions of differential equations driven by processes generated by divergence form operators. In this article, we study a convergence criterion which implies that one can interchange the integral with the limit of a family of stochastic processes generated by divergence form operators. As a corollary, we identify stochastic integrals constructed with the theory of rough paths with Stratonovich or Itô integrals already constructed for stochastic processes generated by divergence form operators by using time-reversal techniques.


Mathematics Subject Classification. 60H10, 60J60

Key words: Rough paths, stochastic differential equations, stochastic process generated by divergence form operators, Condition UTD, convergence of stochastic integrals


© EDP Sciences, SMAI 2008


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.