{
  "titles": [
    {
      "title": "Global existence for rough differential equations under linear growth conditions"
    }
  ],
  "creators": [
    {
      "name": "Gubinelli, Massimiliano",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "Massimiliano"
    },
    {
      "name": "Lejay, Antoine",
      "nameType": "Personal",
      "familyName": "Lejay",
      "givenName": "Antoine"
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2009,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "1",
  "url": "https://arxiv.org/abs/0905.2399v1",
  "dates": [
    {
      "date": "2009-05-14",
      "dateType": "Issued"
    },
    {
      "date": "2009-05-14",
      "dateType": "Available"
    },
    {
      "date": "2026-11-14",
      "dateType": "Updated"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-tex"
  ],
  "subjects": [
    {
      "subject": "math.PR",
      "subjectScheme": "arXiv"
    }
  ],
  "rightsList": [
    {
      "rights": "arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors",
      "rightsUri": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
    }
  ],
  "descriptions": [
    {
      "description": "We 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.",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:0905.2399v1",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.0905.2399",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    }
  ]
}