The non-linear sewing lemma I : weak formulation

Antoine Brault 1 Antoine Lejay 2, 3
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
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.
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Submitted on : Monday, February 25, 2019 - 1:19:37 PM
Last modification on : Friday, October 11, 2019 - 8:22:43 PM
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  • HAL Id : hal-01716945, version 4
  • ARXIV : 1810.11987



Antoine Brault, Antoine Lejay. The non-linear sewing lemma I : weak formulation. 2018. ⟨hal-01716945v4⟩



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