{"title":"奇异退化 SDEs：摆平性和指数遍历性","authors":"Martin Grothaus , Panpan Ren , Feng-Yu Wang","doi":"10.1016/j.jde.2024.08.060","DOIUrl":null,"url":null,"abstract":"<div><p>The well-posedness and exponential ergodicity are proved for stochastic Hamiltonian systems containing a singular drift term which is locally integrable in the component with noise. As an application, the well-posedness and uniform exponential ergodicity are derived for a class of singular degenerated McKean-Vlasov SDEs.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"413 ","pages":"Pages 632-661"},"PeriodicalIF":2.3000,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Singular degenerate SDEs: Well-posedness and exponential ergodicity\",\"authors\":\"Martin Grothaus , Panpan Ren , Feng-Yu Wang\",\"doi\":\"10.1016/j.jde.2024.08.060\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The well-posedness and exponential ergodicity are proved for stochastic Hamiltonian systems containing a singular drift term which is locally integrable in the component with noise. As an application, the well-posedness and uniform exponential ergodicity are derived for a class of singular degenerated McKean-Vlasov SDEs.</p></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":\"413 \",\"pages\":\"Pages 632-661\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-12-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022039624005497\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/9/5 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039624005497","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/9/5 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Singular degenerate SDEs: Well-posedness and exponential ergodicity
The well-posedness and exponential ergodicity are proved for stochastic Hamiltonian systems containing a singular drift term which is locally integrable in the component with noise. As an application, the well-posedness and uniform exponential ergodicity are derived for a class of singular degenerated McKean-Vlasov SDEs.
期刊介绍：
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics
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