101 citations · 101 across the 1 of their papers we have counts for
5 papers
The non-linear sewing lemma III: Stability and generic properties
Antoine Brault, Antoine Lejay
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 discre…
The non-linear sewing lemma II: Lipschitz continuous formulation
Antoine Brault, Antoine Lejay
We give an unified framework to solve rough differential equations. Based on flows, our approach unifies the former ones developed by Davie, Friz-Victoir and Bailleul. The main ide…
The non-linear sewing lemma I : weak formulation
Antoine Brault, Antoine Lejay
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 c…
Solving rough differential equations with the theory of regularity structures
Antoine Brault
The purpose of this article is to solve rough differential equations with the theory of regularity structures. These new tools recently developed by Martin Hairer for solving semi-…
Uncertainty quantification of inflow boundary condition and proximal arterial stiffness coupled effect on pulse wave propagation in a vascular network
A Brault, L Dumas, D Lucor
SUMMARY This work aims at quantifying the effect of inherent uncertainties from cardiac output on the sensitivity of a human compliant arterial network response based on stochastic…