Integration with respect to Hoelder rough paths of order greater than 1/4: an approach via fractional calculu
Integration with respect to Hoelder rough paths of order greater than 1/4: an approach via fractional calculu
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阶次大于 1/4 的 Hoelder 粗糙路径的积分：通过分数阶微积分的方法
DOI：
10.1007/s13348-020-00305-2
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发表时间：
2021
影响因子：
1.1
通讯作者：
Ito Yu
中科院分区：
文献类型：
--
作者：
原田潤一;Ito Yu
在分数阶微积分的基础上，我们引入了关于Hölder阶粗路径的受控路径积分。我们的积分定义是以分数阶导数的勒贝格积分的形式给出的，而不使用任何离散近似的自变量。我们证明了对于适当的-Hölder粗路和受控路，我们的积分定义与通常由补偿Riemann-Stieltjes和的极限给出的定义是一致的。本文的结果也为几何-Hölder粗路上的1-形式积分提供了一种途径。
On the basis of fractional calculus, we introduce an integral of controlled paths with respect to Hölder rough paths of order. Our definition of the integral is given explicitly in terms of Lebesgue integrals for fractional derivatives, without using any arguments from discrete approximation. We demonstrate that for suitable classes of-Hölder rough paths and controlled paths, our definition of the integral is consistent with the usual definition given by the limit of the compensated Riemann–Stieltjes sum. The results of this paper also provide an approach to the integral of 1-forms against geometric-Hölder rough paths.