{"title":"具有随机噪声的微分延迟方程的均方指数稳定性结果。","authors":"Quân Nguyễn Như","doi":"10.51453/2354-1431/2023/849","DOIUrl":null,"url":null,"abstract":"In the present paper, we aim to study of a class of nonlinear differential equations with stochastic noise. Firstly, we introduce the condition of local Lipschitz and a new non-linear growth condition. Then by applying Lyapunov function and semi-martingale convergence theorem, we prove that the stochastic system under consideration has a unique global solution. Additionally, we also investigate the exponential stability of the mean square.","PeriodicalId":158754,"journal":{"name":"SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A RESULT OF MEAN SQUARE EXPONENTIAL STABILITY FOR DIFFERENTIAL DELAY EQUATIONS WITH STOCHASTIC NOISE.\",\"authors\":\"Quân Nguyễn Như\",\"doi\":\"10.51453/2354-1431/2023/849\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present paper, we aim to study of a class of nonlinear differential equations with stochastic noise. Firstly, we introduce the condition of local Lipschitz and a new non-linear growth condition. Then by applying Lyapunov function and semi-martingale convergence theorem, we prove that the stochastic system under consideration has a unique global solution. Additionally, we also investigate the exponential stability of the mean square.\",\"PeriodicalId\":158754,\"journal\":{\"name\":\"SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.51453/2354-1431/2023/849\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.51453/2354-1431/2023/849","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A RESULT OF MEAN SQUARE EXPONENTIAL STABILITY FOR DIFFERENTIAL DELAY EQUATIONS WITH STOCHASTIC NOISE.
In the present paper, we aim to study of a class of nonlinear differential equations with stochastic noise. Firstly, we introduce the condition of local Lipschitz and a new non-linear growth condition. Then by applying Lyapunov function and semi-martingale convergence theorem, we prove that the stochastic system under consideration has a unique global solution. Additionally, we also investigate the exponential stability of the mean square.
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