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

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2023-01-01 DOI:10.2206/kyushujm.77.367

Yu ITO

引用次数: 0

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.

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粗糙积分的反向表示:一种基于分数微积分的方法

在分数阶微积分的基础上，以分数阶导数算子的勒贝格积分形式明确地给出了沿Hölder粗糙路径的控制路径的积分，而不使用任何离散近似的参数。本文从粗糙积分的后向表示的角度，引入了该积分的后向形式，并给出了两个积分之间的基本关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.