Global existence for rough differential equations under linear growth conditions

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dc.creatorGubinelli, Massimiliano
dc.creatorLejay, Antoine
dc.date2009-05-14
dc.date.accessioned2026-07-07T13:15:05Z
dc.date.available2026-07-07T13:15:05Z
dc.descriptionWe prove existence of global solutions for differential equations driven by a geometric rough path under the condition that the vector fields have linear growth. We show by an explicit counter-example that the linear growth condition is not sufficient if the driving rough path is not geometric. This settle a long-standing open question in the theory of rough paths. So in the geometric setting we recover the usual sufficient condition for differential equation. The proof rely on a simple mapping of the differential equation from the Euclidean space to a manifold to obtain a rough differential equation with bounded coefficients.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0905.2399
dc.identifierhttp://arxiv.org/abs/0905.2399
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230380
dc.subjectProbability
dc.titleGlobal existence for rough differential equations under linear growth conditions
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