On Sobolev rough paths
Probability
2021-04-23 v2
Abstract
We introduce the space of rough paths with Sobolev regularity and the corresponding concept of controlled Sobolev paths. Based on these notions, we study rough path integration and rough differential equations. As main result, we prove that the solution map associated to differential equations driven by rough paths is a locally Lipschitz continuous map on the Sobolev rough path space for any arbitrary low regularity and integrability provided .
Cite
@article{arxiv.2006.03322,
title = {On Sobolev rough paths},
author = {Chong Liu and David J. Prömel and Josef Teichmann},
journal= {arXiv preprint arXiv:2006.03322},
year = {2021}
}
Comments
This work is an extended former section of arXiv:1811.05173. Typos corrected, one new remark added