The non-linear sewing lemma II: Lipschitz continuous formulation

Antoine Brault 1 Antoine Lejay 2, 3
3 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : We give an unified framework to solve rough differential equations. Based on flows, our approach unifies the former ones developed by Davie, Friz-Victoir and Bailleul. The main idea is to build a flow from the iterated product of an almost flow which can be viewed as a good approximation of the solution at small time. In this second article, we give some tractable conditions under which the limit flow is Lipschitz continuous and its links with uniqueness of solutions of rough differential equations. We also give perturbation formulas on almost flows which link the former constructions.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [26 references]  Display  Hide  Download
Contributor : Antoine Lejay <>
Submitted on : Friday, October 26, 2018 - 4:28:46 PM
Last modification on : Friday, January 10, 2020 - 9:09:00 PM
Long-term archiving on: Sunday, January 27, 2019 - 1:11:05 PM


Files produced by the author(s)


  • HAL Id : hal-01839202, version 2
  • ARXIV : 1810.11988


Antoine Brault, Antoine Lejay. The non-linear sewing lemma II: Lipschitz continuous formulation. 2018. ⟨hal-01839202v2⟩



Record views


Files downloads