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Constructing general rough differential equations through flow approximations

Antoine Lejay 1, 2
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : 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 by solutions of ordinary differential equations, in the spirit of the backward error analysis. Mixing algebra and analysis, a Taylor formula with remainder and a composition formula are central in the expansion analysis. With a suitable algebraic structure on the non-smooth vector fields to be integrated, we recover in a single framework several results regarding high-order expansions for various kind of driving paths. We also extend the notion of driving rough path. We also introduce as an example a new family of branched rough paths, called aromatic rough paths modeled after aromatic Butcher series.
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https://hal.inria.fr/hal-02871886
Contributor : Antoine Lejay <>
Submitted on : Tuesday, August 4, 2020 - 6:52:09 PM
Last modification on : Friday, August 7, 2020 - 9:23:32 AM

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  • HAL Id : hal-02871886, version 2
  • ARXIV : 2006.10309

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Antoine Lejay. Constructing general rough differential equations through flow approximations. 2020. ⟨hal-02871886v2⟩

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