Sensitivity of rough differential equations
Laure Coutin, Antoine Lejay · 2013
In the context of rough paths theory, we study the regularity of the Ito map with respect to the starting point, the coefficients and perturbation of the driving rough paths. In particular, we show that the Ito map is differentiable with a Holder 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 Holder regularity of the Ito map is established.