Global solutions to rough differential equations with unbounded vector fields

Antoine Lejay 1, 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : We give a sufficient condition to ensure the global existence of a solution to a rough differential equation whose vector field has a linear growth. This condition is slightly weaker than the ones already given and may be used for geometric as well as non-geometric rough paths with values in any suitable (finite or infinite dimensional) space. For this, we study the properties the Euler scheme as done in the work of A.M. Davie.
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Antoine Lejay. Global solutions to rough differential equations with unbounded vector fields. Catherine Donati-Martin and Antoine Lejay and Alain Rouault. Séminaire de Probabilités XLIV, 2046, Springer, pp.215-246, 2012, Lecture Notes in Mathemics, 978-3-642-27460-2. ⟨10.1007/978-3-642-27461-9_11⟩. ⟨inria-00451193v3⟩

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