Perturbed linear rough differential equations

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 : We study linear rough differential equations and we solve perturbed linear rough differential equation using the Duhamel principle. These results provide us with the key technical point to study the regularity of the differential of the Itô map in a subsequent article. Also, the notion of linear rough differential equations leads to consider multiplicative functionals with values in Banach algebra more general than tensor algebra and to consider extensions of classical results such as the Magnus and the Chen-Strichartz formula.
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Laure Coutin, Antoine Lejay. Perturbed linear rough differential equations. Annales mathématiques Blaise Pascal, cedram, 2014, 21 (1), pp.103-150. ⟨10.5802/ambp.338⟩. ⟨hal-00722900v3⟩

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