{"title":"具有相互作用的随机微分方程解的渐近性质","authors":"M. Belozerova","doi":"10.37863/tsp-4121179069-28","DOIUrl":null,"url":null,"abstract":"\nTwo-dimensional stochastic differential equation with interaction is considered.\nThe large time behavior of the distance between two solutions starting from different points is studied.\nA nonzero limit that characterize this distance together with the analogue of the triangle inequality for the map that characterize the limit distance are obtained.\n","PeriodicalId":38143,"journal":{"name":"Theory of Stochastic Processes","volume":"187 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Asymptotic behavior of solutions to stochastic differential equations with interaction\",\"authors\":\"M. Belozerova\",\"doi\":\"10.37863/tsp-4121179069-28\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\nTwo-dimensional stochastic differential equation with interaction is considered.\\nThe large time behavior of the distance between two solutions starting from different points is studied.\\nA nonzero limit that characterize this distance together with the analogue of the triangle inequality for the map that characterize the limit distance are obtained.\\n\",\"PeriodicalId\":38143,\"journal\":{\"name\":\"Theory of Stochastic Processes\",\"volume\":\"187 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Stochastic Processes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37863/tsp-4121179069-28\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Stochastic Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37863/tsp-4121179069-28","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Asymptotic behavior of solutions to stochastic differential equations with interaction
Two-dimensional stochastic differential equation with interaction is considered.
The large time behavior of the distance between two solutions starting from different points is studied.
A nonzero limit that characterize this distance together with the analogue of the triangle inequality for the map that characterize the limit distance are obtained.
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