Sensitivity of rough differential equations: an approach through the omega lemma. (English) Zbl 1423.60088
The authors here mainly rely on the notion of controlled rough path of M. Gubinelli [J. Funct. Anal. 216, No. 1, 86–140 (2004; Zbl 1058.60037)]. They consider the differentiability properties, understood as Fréchet differentiability, of the Ito map under minimal regularity conditions on the vector field. They extend the current results by proving Holder continuity of the Itô map and this generalizes to \(2 \leq p <3\) the results of X.-D. Li and T. J. Lyons [Ann. Sci. Éc. Norm. Supér. (4) 39, No. 4, 649–677 (2006; Zbl 1127.60033)].
Reviewer: Nikolaos Halidias (Athens)
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 60H05 | Stochastic integrals |
Keywords:
rough paths; rough differential equations; Itô map; Malliavin calculus; flow of diffeomorphismsReferences:
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