| Issue |
ESAIM: PS
Volume 12, April 2008
|
|
|---|---|---|
| Page(s) | 387 - 411 | |
| DOI | https://doi.org/10.1051/ps:2007040 | |
| Published online | 25 July 2008 | |
Stochastic differential equations driven by processes generated by divergence form operators II: convergence results
Projet TOSCA,
INRIA & Institut Élie Cartan UMR 7502,
Nancy-Université, CNRS, INRIA.
Campus scientifique, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France; Antoine.Lejay@iecn.u-nancy.fr
Received:
12
September
2007
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.