Abstract
In this note we introduce the notion of Newton–Côtes functionals corrected by Lévy areas, which enables us to consider integrals of the type ∫ f(y) dx, where f is a C2m function and x, y are real Hölderian functions with index α>1/(2m+1) for all m∈ℕ*. We show that this concept extends the Newton–Côtes functional introduced in Gradinaru et al., to a larger class of integrands. Then we give a theorem of existence and uniqueness for differential equations driven by x, interpreted using the symmetric Russo–Vallois integral.
Citation
Ivan Nourdin. Thomas Simon. "Correcting Newton–Côtes integrals by Lévy areas." Bernoulli 13 (3) 695 - 711, August 2007. https://doi.org/10.3150/07-BEJ6015
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