The non-linear sewing lemma I : weak formulation

Abstract : We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak conditions, even solutions to the corresponding rough differential equations are not unique. We show that under additional conditions of the approximation, there exists a unique Lipschitz flow. Then, a perturbation formula is given. Finally, we link our approach to the additive, multiplicative sewing lemmas and the rough Euler scheme.
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal.inria.fr/hal-01716945
Contributor : Antoine Lejay <>
Submitted on : Wednesday, May 15, 2019 - 4:09:00 PM
Last modification on : Friday, January 10, 2020 - 9:09:02 PM

Files

non-linear-sewing-lemma-I-FV.p...
Files produced by the author(s)

Identifiers

Citation

Antoine Brault, Antoine Lejay. The non-linear sewing lemma I : weak formulation. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), In press, 24 (59), pp.1-24. ⟨10.1214/19-EJP313⟩. ⟨hal-01716945v5⟩

Share

Metrics

Record views

207

Files downloads

1068