Global existence for rough differential equations under linear growth conditions

Massimiliano Gubinelli; Antoine Lejay

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arXiv · 0905.2399

Global existence for rough differential equations under linear growth conditions

Massimiliano Gubinelli·Antoine Lejay

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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.

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Massimiliano Gubinelli, Antoine Lejay. 2009-05-14. Global existence for rough differential equations under linear growth conditions. https://arxiv.org/abs/0905.2399

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