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2020 Rough integration via fractional calculus
Yu Ito
Tohoku Math. J. (2) 72(1): 39-62 (2020). DOI: 10.2748/tmj/1585101620

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

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Yu Ito. "Rough integration via fractional calculus." Tohoku Math. J. (2) 72 (1) 39 - 62, 2020. https://doi.org/10.2748/tmj/1585101620

Information

Published: 2020
First available in Project Euclid: 25 March 2020

zbMATH: 07199986
MathSciNet: MR4079423
Digital Object Identifier: 10.2748/tmj/1585101620

Subjects:
Primary: 26A42
Secondary: 26A33, 60H05

Rights: Copyright © 2020 Tohoku University

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Vol.72 • No. 1 • 2020
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