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2019 The non-linear sewing lemma I: weak formulation
Antoine Brault, Antoine Lejay
Electron. J. Probab. 24: 1-24 (2019). DOI: 10.1214/19-EJP313

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 if 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.

Citation

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Antoine Brault. Antoine Lejay. "The non-linear sewing lemma I: weak formulation." Electron. J. Probab. 24 1 - 24, 2019. https://doi.org/10.1214/19-EJP313

Information

Received: 27 February 2018; Accepted: 2 May 2019; Published: 2019
First available in Project Euclid: 21 June 2019

zbMATH: 07088997
MathSciNet: MR3978209
Digital Object Identifier: 10.1214/19-EJP313

Subjects:
Primary: 54C65, 60H10

JOURNAL ARTICLE
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