Perturbed linear rough differential equations

Coutin, Laure; Lejay, Antoine

Annales mathématiques Blaise Pascal, Tome 21 (2014) no. 1, pp. 103-150.

Nous étudions les équations différentielles linéaires rugueuses et résolvons des équations linéaires rugueuses perturbées à l’aide du principe de Duhamel. Ces résultats donnent un argument technique pour étudier la différentiabilité de l’application d’Itô. La notion d’équation différentielle rugueuses nous condition à considérer des fonctionnelles multiplicatives à valeurs dans des algèbres de Banach plus générales que celle des algèbres tensorielles, ainsi que des extensions de résultats classiques tels que les formules de Magnus et Chen-Strichartz.

We study linear rough differential equations and we solve perturbed linear rough differential equations using the Duhamel principle. These results provide us with a 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 algebras more general than tensor algebras and to consider extensions of classical results such as the Magnus and the Chen-Strichartz formula.

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