Regularity of the Ito-Lyons map
Probability
2015-04-30 v3 Classical Analysis and ODEs
Abstract
We show in this note that the Ito-Lyons solution map associated to a rough differential equation is Frechet differentiable when understood as a map between some Banach spaces of controlled paths. This regularity result provides an elementary approach to Taylor-like expansions of Inahama-Kawabi type for solutions of rough differential equations depending on a small parameter, and makes the construction of some natural dynamics on the path space over any compact Riemannian manifold straightforward, giving back Driver's flow as a particular case.
Keywords
Cite
@article{arxiv.1401.1147,
title = {Regularity of the Ito-Lyons map},
author = {I. Bailleul},
journal= {arXiv preprint arXiv:1401.1147},
year = {2015}
}
Comments
Final version, 11 pages. An integration by parts formula for the Ito-Lyons map has been added as another application of the main result