Linear Rough Differential Equations

Antoine Lejay (Université de Lorraine, Nancy, Frankreich)
Wednesday, December 11, 2013 - 5:00pm
Erhard-Schmidt-Hörsaal, Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin

Although linear Rough Differential Equations (LRDE) could be seen as a particular case of Rough Differential Equations (RDE), they are worth to be considered as objects with their specific properties. Following the work of D. Feyel, A. de la Pradelles and G. Mokobodzki, we present in this talk a coherent theory of LRDE by considering rough resolvent (or semi-group, propagators) in Banach algebra. A particular well-known case is the one of rough paths, by specializing the underlying space to tensor algebra. The Magnus formula in this rough setting, as well as Duhamel principle are also studied. The latter one could be used to provide us with alternative proofs on the differentiability of the Ito map.