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Book Sections Year : 2012

Global solutions to rough differential equations with unbounded vector fields

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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Dates and versions

inria-00451193 , version 1 (28-01-2010)
inria-00451193 , version 2 (22-03-2010)
inria-00451193 , version 3 (22-08-2012)

Identifiers

Cite

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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