## Kyoto Journal of Mathematics

### A fractional calculus approach to rough integration

Yu Ito

#### Abstract

On the basis of fractional calculus, we introduce an integral of controlled paths against $\beta$-Hölder rough paths with $\beta \in (1/3,1/2]$. 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.

#### Article information

Source
Kyoto J. Math., Volume 59, Number 3 (2019), 553-573.

Dates
Revised: 31 March 2017
Accepted: 6 April 2017
First available in Project Euclid: 17 May 2019

https://projecteuclid.org/euclid.kjm/1558059097

Digital Object Identifier
doi:10.1215/21562261-2019-0017

Mathematical Reviews number (MathSciNet)
MR3990177

Zentralblatt MATH identifier
07108002

#### Citation

Ito, Yu. A fractional calculus approach to rough integration. Kyoto J. Math. 59 (2019), no. 3, 553--573. doi:10.1215/21562261-2019-0017. https://projecteuclid.org/euclid.kjm/1558059097

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