Sensitivity of rough differential equations: An approach through the Omega lemma |
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Authors: | Laure Coutin Antoine Lejay |
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Affiliation: | 1. Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, UT3, France;2. Université de Lorraine, IECL, UMR 7502, Vand?uvre-lès-Nancy, F-54600, France;3. CNRS, IECL, UMR 7502, Vand?uvre-lès-Nancy, F-54600, France;4. Inria, Villers-lès-Nancy, F-54600, France |
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Abstract: | The Itô map gives the solution of a Rough Differential Equation, a generalization of an Ordinary Differential Equation driven by an irregular path, when existence and uniqueness hold. By studying how a path is transformed through the vector field which is integrated, we prove that the Itô map is Hölder or Lipschitz continuous with respect to all its parameters. This result unifies and weakens the hypotheses of the regularity results already established in the literature. |
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Keywords: | Rough paths Rough differential equations Itô map Malliavin calculus Flow of diffeomorphisms |
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