### References & Citations

# Mathematics > Probability

# Title: The Sewing lemma for $0 < γ\leq 1$

(Submitted on 13 Oct 2021 (v1), last revised 16 Nov 2021 (this version, v2))

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 Lyons-Victoir extension theorem which associates to a H\"older 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 H\"older functions on the set of Rough Paths.

## Submission history

From: Lucas Broux [view email]**[v1]**Wed, 13 Oct 2021 16:40:05 GMT (36kb,D)

**[v2]**Tue, 16 Nov 2021 13:50:22 GMT (38kb,D)

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