BACKWARD REPRESENTATION OF ROUGH INTEGRAL: AN APPROACH BASED ON FRACTIONAL CALCULUS
BACKWARD REPRESENTATION OF ROUGH INTEGRAL: AN APPROACH BASED ON FRACTIONAL CALCULUS
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通讯作者：
YU Ito
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作者：
YU Ito
。在分数阶微积分的基础上，给出了沿H(CID：127)条较老的粗糙路径的受控路径的积分显式地表示为分数阶导数算子的勒贝格积分，而不使用任何离散近似的变元.本文从粗积分的向后表示的角度出发，引入了一种向后形式的积分，并给出了两种积分之间的基本关系。
. On the basis of fractional calculus, the integral of controlled paths along H(cid:127)older 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 back-ward representation of the rough integral.