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On (p,q)-rough paths

Antoine Lejay 1, 2 Nicolas Victoir 3
2 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : We extend the work of T. Lyons (1998) and T. Lyons and Z. Qian (2002) to define integrals and solutions of differential equations along product of p and q rough paths, with 1/p+1/q>1. We use this to write an Itô formula at the level of rough paths, and to see that any rough path can always be interpreted as a product of a p-geometric rough path and a p/2-geometric rough path.
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Submitted on : Sunday, September 10, 2006 - 11:13:20 AM
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Antoine Lejay, Nicolas Victoir. On (p,q)-rough paths. Journal of Differential Equations, Elsevier, 2006, 225 (1), pp.103-133. ⟨10.1016/j.jde.2006.01.018⟩. ⟨inria-00092420⟩



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