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On rough differential equations. (English) Zbl 1190.60044

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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
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