Sensitivity of rough differential equations: an approach through the Omega lemma
Probability
2019-05-01 v1
Abstract
The It{\^o} map assigns the solution of a Rough Differential Equation, a generalization of an Ordinary Differential Equation driven by an irregular path, when existence and uniqueness hold. By studying how a path is transformed through the vector field which is integrated, we prove that the It{\^o} map is H{\"o}lder or Lipschitz continuous with respect to all its parameters. This result unifies and weaken the hypotheses of the regularity results already established in the literature.
Keywords
Cite
@article{arxiv.1712.04705,
title = {Sensitivity of rough differential equations: an approach through the Omega lemma},
author = {Laure Coutin and Antoine Lejay},
journal= {arXiv preprint arXiv:1712.04705},
year = {2019}
}
Comments
Journal of Differential Equations, Elsevier, A Para{\^i}tre