{"title":"一类Rosenblatt过程驱动的随机泛函积分微分系统的存在性结果","authors":"Amadou Diop, Mamadou Abdoul Diop, Khalil Ezzinbi, Essozimna Kpizim","doi":"10.1515/rose-2023-2020","DOIUrl":null,"url":null,"abstract":"Abstract This work investigates the existence and uniqueness of mild solutions to a class of stochastic integral differential equations with various time delay driven by the Rosenblatt process. We can obtain alternative conditions that guarantee mild solutions by using the resolvent operator in the Grimmer sense, stochastic analysis, fixed-point methods, and noncompact measures. We give an example to illustrate the theory.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"7 12","pages":"0"},"PeriodicalIF":0.3000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence results for some stochastic functional integrodifferential systems driven by Rosenblatt process\",\"authors\":\"Amadou Diop, Mamadou Abdoul Diop, Khalil Ezzinbi, Essozimna Kpizim\",\"doi\":\"10.1515/rose-2023-2020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract This work investigates the existence and uniqueness of mild solutions to a class of stochastic integral differential equations with various time delay driven by the Rosenblatt process. We can obtain alternative conditions that guarantee mild solutions by using the resolvent operator in the Grimmer sense, stochastic analysis, fixed-point methods, and noncompact measures. We give an example to illustrate the theory.\",\"PeriodicalId\":43421,\"journal\":{\"name\":\"Random Operators and Stochastic Equations\",\"volume\":\"7 12\",\"pages\":\"0\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Operators and Stochastic Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/rose-2023-2020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Operators and Stochastic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/rose-2023-2020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Existence results for some stochastic functional integrodifferential systems driven by Rosenblatt process
Abstract This work investigates the existence and uniqueness of mild solutions to a class of stochastic integral differential equations with various time delay driven by the Rosenblatt process. We can obtain alternative conditions that guarantee mild solutions by using the resolvent operator in the Grimmer sense, stochastic analysis, fixed-point methods, and noncompact measures. We give an example to illustrate the theory.
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