{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266124060016\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124060016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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.
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