The non-linear sewing lemma II: Lipschitz continuous formulation

Antoine Brault (1) , Antoine Lejay (2, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IECL - Institut Élie Cartan de Lorraine
3 TOSCA - TO Simulate and CAlibrate stochastic models

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 idea is to build a flow from the iterated product of an almost flow which can be viewed as a good approximation of the solution at small time. In this second article, we give some tractable conditions under which the limit flow is Lipschitz continuous and its links with uniqueness of solutions of rough differential equations. We also give perturbation formulas on almost flows which link the former constructions.

Mots clés: Rough differential equations; Lipschitz flows; Rough paths

Domaines: Probabilités [math.PR]; Analyse classique [math.CA]

Antoine Brault, Antoine Lejay. The non-linear sewing lemma II: Lipschitz continuous formulation. 2018. ⟨hal-01839202v2⟩