Global existence for rough differential equations under linear growth conditionsReport as inadecuate




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1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision 2 IECN - Institut Élie Cartan de Nancy 3 TOSCA INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502

Abstract : 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.





Author: Massimiliano Gubinelli - Antoine Lejay -

Source: https://hal.archives-ouvertes.fr/



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