{"title":"非线性随机Ito-Volterra积分方程的Ulam-Hyers-Rassias稳定性","authors":"Ngo Phuoc Nguyen Ngoc, N. Vinh","doi":"10.7153/DEA-2018-10-27","DOIUrl":null,"url":null,"abstract":"In this paper, by using the classical Banach contraction principle, we investigate and establish the stability in the sense of Ulam-Hyers and in the sense of Ulam-Hyers-Rassias for the following stochastic integral equation Xt = ξt + ∫ t 0 A(t,s,Xs)ds+ ∫ t 0 B(t,s,Xs)dWs, where ∫ t 0 B(t,s,Xs)dWs is Ito integral.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"6 1","pages":"397-411"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Ulam-Hyers-Rassias stability of a nonlinear stochastic Ito-Volterra integral equation\",\"authors\":\"Ngo Phuoc Nguyen Ngoc, N. Vinh\",\"doi\":\"10.7153/DEA-2018-10-27\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, by using the classical Banach contraction principle, we investigate and establish the stability in the sense of Ulam-Hyers and in the sense of Ulam-Hyers-Rassias for the following stochastic integral equation Xt = ξt + ∫ t 0 A(t,s,Xs)ds+ ∫ t 0 B(t,s,Xs)dWs, where ∫ t 0 B(t,s,Xs)dWs is Ito integral.\",\"PeriodicalId\":11162,\"journal\":{\"name\":\"Differential Equations and Applications\",\"volume\":\"6 1\",\"pages\":\"397-411\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/DEA-2018-10-27\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/DEA-2018-10-27","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ulam-Hyers-Rassias stability of a nonlinear stochastic Ito-Volterra integral equation
In this paper, by using the classical Banach contraction principle, we investigate and establish the stability in the sense of Ulam-Hyers and in the sense of Ulam-Hyers-Rassias for the following stochastic integral equation Xt = ξt + ∫ t 0 A(t,s,Xs)ds+ ∫ t 0 B(t,s,Xs)dWs, where ∫ t 0 B(t,s,Xs)dWs is Ito integral.
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