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Global existence for rough differential equations under linear growth conditions

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Date
2009-05
Link to item file
http://hal.archives-ouvertes.fr/hal-00384327/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
Rough differential equation; Global existence; Change of variable formula; Explosion in a finite time; Rough path; Geometric rough paths
URI
https://basepub.dauphine.fr/handle/123456789/3051
Collections
  • CEREMADE : Publications
Metadata
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Author
Gubinelli, Massimiliano
Lejay, Antoine
Type
Document de travail / Working paper
Item number of pages
20 pages
Abstract (EN)
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.

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