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September 2019 A fractional calculus approach to rough integration
Yu Ito
Kyoto J. Math. 59(3): 553-573 (September 2019). DOI: 10.1215/21562261-2019-0017

Abstract

On the basis of fractional calculus, we introduce an integral of controlled paths against β-Hölder rough paths with β(1/3,1/2]. The integral is defined by the Lebesgue integrals for fractional derivative operators, without using any argument based on discrete approximation. We show in this article that the integral is consistent with that obtained by the usual integration in rough path analysis, given by the limit of the compensated Riemann–Stieltjes sums.

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Yu Ito. "A fractional calculus approach to rough integration." Kyoto J. Math. 59 (3) 553 - 573, September 2019. https://doi.org/10.1215/21562261-2019-0017

Information

Received: 18 December 2016; Revised: 31 March 2017; Accepted: 6 April 2017; Published: September 2019
First available in Project Euclid: 17 May 2019

zbMATH: 07108002
MathSciNet: MR3990177
Digital Object Identifier: 10.1215/21562261-2019-0017

Subjects:
Primary: 26A42
Secondary: 26A33

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 3 • September 2019
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