{"title":"针对 $$L^p$$ 空间中卡普托随机分微分方程的几类 Carathéodory 方案","authors":"Phan Thi Huong, Pham The Anh","doi":"10.1007/s40306-023-00518-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we construct Carathéodory type and exponential Carathéodory type schemes for Caputo stochastic fractional differential equations (CSFDEs) of order <span>\\(\\alpha \\in (\\frac{1}{2},1)\\)</span> in <span>\\(L^p\\)</span> spaces with <span>\\(p \\ge 2\\)</span> whose coefficients satisfy a standard Lipschitz and a linear growth bound conditions. The strong convergence and the convergence rate of these schemes are also established.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Types of Carathéodory Scheme for Caputo Stochastic Fractional Differential Equations in \\\\(L^p\\\\) Spaces\",\"authors\":\"Phan Thi Huong, Pham The Anh\",\"doi\":\"10.1007/s40306-023-00518-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we construct Carathéodory type and exponential Carathéodory type schemes for Caputo stochastic fractional differential equations (CSFDEs) of order <span>\\\\(\\\\alpha \\\\in (\\\\frac{1}{2},1)\\\\)</span> in <span>\\\\(L^p\\\\)</span> spaces with <span>\\\\(p \\\\ge 2\\\\)</span> whose coefficients satisfy a standard Lipschitz and a linear growth bound conditions. The strong convergence and the convergence rate of these schemes are also established.</p></div>\",\"PeriodicalId\":45527,\"journal\":{\"name\":\"Acta Mathematica Vietnamica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Vietnamica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40306-023-00518-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-023-00518-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Some Types of Carathéodory Scheme for Caputo Stochastic Fractional Differential Equations in \(L^p\) Spaces
In this paper, we construct Carathéodory type and exponential Carathéodory type schemes for Caputo stochastic fractional differential equations (CSFDEs) of order \(\alpha \in (\frac{1}{2},1)\) in \(L^p\) spaces with \(p \ge 2\) whose coefficients satisfy a standard Lipschitz and a linear growth bound conditions. The strong convergence and the convergence rate of these schemes are also established.
期刊介绍:
Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.