The non-linear sewing lemma I: weak formulation

A 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.
Type de document :
Pré-publication, Document de travail
The authors are grateful to the CIRM (Marseille, France) for its kind hospitality with the Resear.. 2018
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Dernière modification le : vendredi 14 septembre 2018 - 09:16:06
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  • HAL Id : hal-01716945, version 1

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A Brault, Antoine Lejay. The non-linear sewing lemma I: weak formulation. The authors are grateful to the CIRM (Marseille, France) for its kind hospitality with the Resear.. 2018. 〈hal-01716945v1〉

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