The Sewing lemma for $0 < \gamma \leq 1$
Abstract
We establish a Sewing lemma in the regime $\gamma \in \left( 0, 1 \right]$, constructing a Sewing map which is neither unique nor canonical, but which is nonetheless continuous with respect to the standard norms. Two immediate corollaries follow, which hold on any commutative graded connected locally finite Hopf algebra: a simple constructive proof of the LyonsVictoir extension theorem which associates to a Hölder path a rough path, with the additional result that this map can be made continuous; the bicontinuity of a transitive free action of a space of Hölder functions on the set of Rough Paths.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.06928
 Bibcode:
 2021arXiv211006928B
 Keywords:

 Mathematics  Probability
 EPrint:
 31 pages