• Bernoulli
  • Volume 13, Number 3 (2007), 695-711.

Correcting Newton–Côtes integrals by Lévy areas

Ivan Nourdin and Thomas Simon

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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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Bernoulli, Volume 13, Number 3 (2007), 695-711.

First available in Project Euclid: 7 August 2007

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fractional Brownian motion Lévy area Newton–Côtes integral rough differential equation symmetric stochastic integral


Nourdin, Ivan; Simon, Thomas. Correcting Newton–Côtes integrals by Lévy areas. Bernoulli 13 (2007), no. 3, 695--711. doi:10.3150/07-BEJ6015.

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