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August 2007 Correcting Newton–Côtes integrals by Lévy areas
Ivan Nourdin, Thomas Simon
Bernoulli 13(3): 695-711 (August 2007). DOI: 10.3150/07-BEJ6015

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.

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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

Information

Published: August 2007
First available in Project Euclid: 7 August 2007

zbMATH: 1132.60047
MathSciNet: MR2348747
Digital Object Identifier: 10.3150/07-BEJ6015

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

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Vol.13 • No. 3 • August 2007
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