Correcting Newton-Côtes integrals by Lévy areas
Résumé
In this note we introduce the notion of Newton-Côtes integral corrected by Lévy areas, which enables us to consider integrals of the type $\int f(y) dx,$ where f is a $C^{2m}$ function and x, y are real Hölderian functions with index > 1/(2m+1), for any integer m. We show that this concept extends the Newton-Côtes integral introduced in (Gradinaru et al., Ann. Inst. H. Poincaré Probab. Statist. 41 (4), 781-806, 2005), to a larger class of integrands. Then, we give a theorem of existence and uniqueness for differential equations driven by x, interpreted using this new integral.
Loading...