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.
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Submitted on : Friday, October 26, 2018 - 4:28:46 PM
Last modification on : Friday, April 19, 2019 - 4:55:12 PM
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  • HAL Id : hal-01839202, version 2
  • ARXIV : 1810.11988

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

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