BACKWARD REPRESENTATION OF THE ROUGH INTEGRAL: AN APPROACH BASED ON FRACTIONAL CALCULUS

Abstract

On the basis of fractional calculus, the integral of controlled paths along Hölder rough paths is given explicitly as Lebesgue integrals for fractional derivative operators, without using any arguments from a discrete approximation. In this paper, we introduce a backward version of the integral and provide fundamental relations between both integrals from the perspective of the backward representation of the rough integral.