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• W2998574173 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 using a non-linear sewing lemma. In this article, we show that such solutions also solve a fixed point problem by exhibiting a suitable functional. Convergence then follows from consistency and stability, two notions that are adapted to our framework. In addition, we show that uniqueness and convergence of discrete approximations is a generic property, meaning that it holds excepted for a set of vector fields and starting points which is of Baire first category. At last, we show that Brownian flows are almost surely unique solutions to RDE associated to Lipschitz flows. The later property yields almost sure convergence of Milstein schemes." @default.
• W2998574173 created "2020-01-10" @default.
• W2998574173 creator A5040774808 @default.
• W2998574173 creator A5083621910 @default.
• W2998574173 date "2020-04-24" @default.
• W2998574173 modified "2023-09-27" @default.
• W2998574173 title "The non-linear sewing lemma III: Stability and generic properties" @default.
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• W2998574173 hasPublicationYear "2020" @default.
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