分数阶随机volterra积分微分方程解的Hurst指数中的Lipschitz连续性

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications Pub Date : 2023-07-04 DOI:10.1080/07362994.2022.2075385

Nguyen Tien Dung, Ta Cong Son

{"title":"分数阶随机volterra积分微分方程解的Hurst指数中的Lipschitz连续性","authors":"Nguyen Tien Dung, Ta Cong Son","doi":"10.1080/07362994.2022.2075385","DOIUrl":null,"url":null,"abstract":"Abstract The problem of investigating the continuity in the Hurst index arises naturally in statistical inferences related to fractional Brownian motion. In this paper, based on the techniques of the Malliavin calculus, we introduce a method to deal with this problem. We first provide an explicit bound on the difference between two non-smooth functionals of Malliavin differentiable random variables. Then, we apply the obtained bound to show Lipchitz continuity of fractional stochastic Volterra integro-differential equations and its additive functionals.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"693 - 712"},"PeriodicalIF":0.8000,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Lipschitz continuity in the Hurst index of the solutions of fractional stochastic volterra integro-differential equations\",\"authors\":\"Nguyen Tien Dung, Ta Cong Son\",\"doi\":\"10.1080/07362994.2022.2075385\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The problem of investigating the continuity in the Hurst index arises naturally in statistical inferences related to fractional Brownian motion. In this paper, based on the techniques of the Malliavin calculus, we introduce a method to deal with this problem. We first provide an explicit bound on the difference between two non-smooth functionals of Malliavin differentiable random variables. Then, we apply the obtained bound to show Lipchitz continuity of fractional stochastic Volterra integro-differential equations and its additive functionals.\",\"PeriodicalId\":49474,\"journal\":{\"name\":\"Stochastic Analysis and Applications\",\"volume\":\"41 1\",\"pages\":\"693 - 712\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastic Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/07362994.2022.2075385\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/07362994.2022.2075385","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 3

摘要

研究Hurst指数的连续性的问题自然出现在与分数布朗运动有关的统计推断中。本文在Malliavin微积分技术的基础上，介绍了一种处理这一问题的方法。我们首先给出了Malliavin可微随机变量的两个非光滑泛函之间差的一个显式界。然后，我们应用所得的界来证明分数阶随机Volterra积分微分方程及其加性泛函的Lipchitz连续性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Lipschitz continuity in the Hurst index of the solutions of fractional stochastic volterra integro-differential equations

Abstract The problem of investigating the continuity in the Hurst index arises naturally in statistical inferences related to fractional Brownian motion. In this paper, based on the techniques of the Malliavin calculus, we introduce a method to deal with this problem. We first provide an explicit bound on the difference between two non-smooth functionals of Malliavin differentiable random variables. Then, we apply the obtained bound to show Lipchitz continuity of fractional stochastic Volterra integro-differential equations and its additive functionals.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Stochastic Analysis and Applications 数学-统计学与概率论

CiteScore

2.70

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.