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Journal Articles Electronic Journal of Probability Year : 2019

The non-linear sewing lemma I : weak formulation


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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Dates and versions

hal-01716945 , version 1 (25-02-2018)
hal-01716945 , version 2 (26-10-2018)
hal-01716945 , version 3 (25-02-2019)
hal-01716945 , version 4 (25-02-2019)
hal-01716945 , version 5 (15-05-2019)



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