The non-linear sewing lemma II: Lipschitz continuous formulation

@article{Brault2018TheNS,
  title={The non-linear sewing lemma II: Lipschitz continuous formulation},
  author={Antoine Brault and Antoine Lejay},
  journal={arXiv: Probability},
  year={2018}
}
The non-linear sewing lemma I: weak formulation
  • A. Brault, A. Lejay
  • Mathematics, Computer Science
    Electronic Journal of Probability
  • 2019
TLDR
It is proved that measurable flows exist under weak conditions, even solutions to the corresponding rough differential equations are not unique, and it is shown that under additional conditions of the approximation, there exists a unique Lipschitz flow.
The non-linear sewing lemma III: Stability and generic properties
Abstract Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme
Constructing general rough differential equations through flow approximations
  • A. Lejay
  • Mathematics
    Electronic Journal of Probability
  • 2022
The non-linear sewing lemma constructs flows of rough differential equations from a braod class of approximations called almost flows. We consider a class of almost flows that could be approximated
On the definition of a solution to a rough differential equation
  • I. Bailleul
  • Mathematics
    Annales de la Faculté des sciences de Toulouse : Mathématiques
  • 2021
We give an elementary proof that Davie's definition of a solution to a rough differential equation and the notion of solution given by Bailleul in (Flows driven by rough paths) coincide. This
Lorentz-equivariant flow with four delays of neutral type
We generalize electrodynamics with a second interaction in lightcone. The timereversible equations for two-body motion define a semiflow on C(R) with four state-dependent delays of neutral type and

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The non-linear sewing lemma I: weak formulation
  • A. Brault, A. Lejay
  • Mathematics, Computer Science
    Electronic Journal of Probability
  • 2019
TLDR
It is proved that measurable flows exist under weak conditions, even solutions to the corresponding rough differential equations are not unique, and it is shown that under additional conditions of the approximation, there exists a unique Lipschitz flow.
The non-linear sewing lemma III: Stability and generic properties
Abstract Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme
Flows driven by rough paths
We devise in this work a simple mechanism for constructing flows on a Banach space from approximate flows, and show how it can be used in a simple way to reprove from scratch and extend the main
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TLDR
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