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dc.contributor.authorGubinelli, Massimiliano
dc.contributor.authorLejay, Antoine
HAL ID: 2358
ORCID: 0000-0003-0406-9550
dc.subjectRough differential equationen
dc.subjectGlobal existenceen
dc.subjectChange of variable formulaen
dc.subjectExplosion in a finite timeen
dc.subjectRough pathen
dc.subjectGeometric rough pathsen
dc.titleGlobal existence for rough differential equations under linear growth conditionsen
dc.typeDocument de travail / Working paper
dc.contributor.editoruniversityotherINRIA – CNRS;France
dc.contributor.editoruniversityotherInstitut Elie Cartan Nancy;France
dc.description.abstractenWe 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.en
dc.identifier.citationpages20 pagesen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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