Global existence for rough differential equations under linear growth conditions

Details Global existence for rough differential equations under linear growth conditions Global existence for rough differential equations under linear growth conditions

2009-05-14

arxiv.org/abs/0905.2399v1

Mathematics

Probability

20 pages

Scientific paper

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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