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

Laure Coutin; Antoine Lejay

doi:10.1016/j.jde.2017.11.03

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arXiv · 1712.04705

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

Laure Coutin·Antoine Lejay

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Abstract

The It{\^o} 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 It{\^o} map is H{\"o}lder or Lipschitz continuous with respect to all its parameters. This result unifies and weaken the hypotheses of the regularity results already established in the literature.

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Laure Coutin, Antoine Lejay. 2017-12-13. Sensitivity of rough differential equations: an approach through the Omega lemma. https://doi.org/10.1016/j.jde.2017.11.03

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