{"title":"粗糙积分的反向表示:一种基于分数微积分的方法","authors":"Yu ITO","doi":"10.2206/kyushujm.77.367","DOIUrl":null,"url":null,"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.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"BACKWARD REPRESENTATION OF THE ROUGH INTEGRAL: AN APPROACH BASED ON FRACTIONAL CALCULUS\",\"authors\":\"Yu ITO\",\"doi\":\"10.2206/kyushujm.77.367\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":49929,\"journal\":{\"name\":\"Kyushu Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kyushu Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2206/kyushujm.77.367\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2206/kyushujm.77.367","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
BACKWARD REPRESENTATION OF THE ROUGH INTEGRAL: AN APPROACH BASED ON FRACTIONAL CALCULUS
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.
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.
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