Sensitivity of rough differential equations: an approach through the Omega lemma

Laure Coutin 1 Antoine Lejay 2, 3
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : The Itô map assigns 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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Submitted on : Tuesday, December 12, 2017 - 4:17:45 PM
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Laure Coutin, Antoine Lejay. Sensitivity of rough differential equations: an approach through the Omega lemma. Journal of Differential Equations, Elsevier, 2018, 264 (6), pp.3899-3917. ⟨10.1016/j.jde.2017.11.031⟩. ⟨hal-00875670v6⟩

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