Abstract
On the basis of fractional calculus, the author's previous study [9] introduced an approach to the integral of controlled paths against Hölder rough paths. The integral in [9] is defined by the Lebesgue integrals for fractional derivatives without using any arguments based on discrete approximation. In this paper, we revisit the approach of [9] and show that, for a suitable class of Hölder rough paths including geometric Hölder rough paths, the integral in [9] is consistent with that obtained by the usual integration theory of rough path analysis, given by the limit of the compensated Riemann–Stieltjes sums.
Citation
Yu Ito. "Rough integration via fractional calculus." Tohoku Math. J. (2) 72 (1) 39 - 62, 2020. https://doi.org/10.2748/tmj/1585101620
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