{"title":"具有赫斯特指数 $$H>1/4 $$ 的分数布朗运动驱动的混合型随机微分方程强解的存在性和唯一性","authors":"M. M. Vas’kovskii, P. P. Stryuk","doi":"10.1134/s0012266124060016","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the unique solvability of the Cauchy problem for a mixed-type stochastic\ndifferential equation driven by the standard Brownian motion and fractional Brownian motions\nwith Hurst exponents <span>\\(H>1/4\\)</span>. We prove a\ntheorem on the existence and uniqueness of strong solutions of these stochastic differential\nequations.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"16 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and Uniqueness of Strong Solutions of Mixed-Type Stochastic Differential Equations Driven by Fractional Brownian Motions with Hurst Exponents $$H>1/4 $$\",\"authors\":\"M. M. Vas’kovskii, P. P. Stryuk\",\"doi\":\"10.1134/s0012266124060016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We study the unique solvability of the Cauchy problem for a mixed-type stochastic\\ndifferential equation driven by the standard Brownian motion and fractional Brownian motions\\nwith Hurst exponents <span>\\\\(H>1/4\\\\)</span>. We prove a\\ntheorem on the existence and uniqueness of strong solutions of these stochastic differential\\nequations.\\n</p>\",\"PeriodicalId\":50580,\"journal\":{\"name\":\"Differential Equations\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266124060016\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124060016","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Existence and Uniqueness of Strong Solutions of Mixed-Type Stochastic Differential Equations Driven by Fractional Brownian Motions with Hurst Exponents $$H>1/4 $$
Abstract
We study the unique solvability of the Cauchy problem for a mixed-type stochastic
differential equation driven by the standard Brownian motion and fractional Brownian motions
with Hurst exponents \(H>1/4\). We prove a
theorem on the existence and uniqueness of strong solutions of these stochastic differential
equations.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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