Differential Equations driven by \Pi-rough paths
Classical Analysis and ODEs
2014-10-07 v4
Abstract
This paper revisits the concept of rough paths of inhomogeneous degree of smoothness (geometric \Pi-rough paths in our terminology) sketched by Lyons ("Differential equations driven by rough signals", Revista Mathematica Iber. Vol 14, Nr. 2,215-310, 1998). Although geometric \Pi-rough paths can be treated as p-rough paths for a sufficiently large p and the theory of integration of Lip-\gamma one-forms (\gamma>p-1) along geometric p-rough paths applies, we prove the existence of integrals of one-forms under weaker conditions. Moreover, we consider differential equations driven by geometric \Pi-rough paths and give sufficient conditions for existence and uniqueness of solution.
Cite
@article{arxiv.1205.1832,
title = {Differential Equations driven by \Pi-rough paths},
author = {Lajos Gergely Gyurkó},
journal= {arXiv preprint arXiv:1205.1832},
year = {2014}
}