Lejay, Antoine On rough differential equations. (English) Zbl 1190.60044 Electron. J. Probab. 14, 341-364 (2009). Summary: We prove that the Itô map, that is the map that gives the solution of a differential equation controlled by a rough path of finite \(p\)-variation with \(p\) in [2,3) is locally Lipschitz continuous in all its arguments and we give some sufficient conditions for global existence for non-bounded vector fields. Cited in 11 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 34F05 Ordinary differential equations and systems with randomness Keywords:rough paths; Itô map; controlled differential equations PDFBibTeX XMLCite \textit{A. Lejay}, Electron. J. Probab. 14, 341--364 (2009; Zbl 1190.60044) Full Text: DOI EuDML EMIS