Abstract
Using fractional calculus, we introduce an integral along β-Hölder rough paths for any β ∈ (0,1]. This is a natural generalization of the Riemann–Stieltjes integral along smooth curves. We prove that, under suitable conditions on the integrand, this integral is a continuous functional with respect to the Hölder topology. As a result, this provides an alternative definition of the first level path of the rough integral along geometric Hölder rough paths.
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This work was partially supported by JSPS Research Fellowships for Young Scientists.
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Ito, Y. Integrals Along Rough Paths via Fractional Calculus. Potential Anal 42, 155–174 (2015). https://doi.org/10.1007/s11118-014-9428-3
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DOI: https://doi.org/10.1007/s11118-014-9428-3