Sensitivity of rough differential equations
Résumé
In the context of rough paths theory,
we study the regularity
of the Itô map with respect to the starting point,
the coefficients and perturbation of the driving rough paths.
In particular, we show that the Itô map
is differentiable with a Hölder or Lipschitz continuous
derivatives under general hypotheses. With respect to the current literature
on the subject, our proof relies on perturbation of linear
Rough Differential Equations, and the Hölder regularity of the Itô map is established.
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