{"title":"有限维和无限维的分布相关随机微分延迟方程","authors":"Rico Heinemann","doi":"10.1142/s0219025720500241","DOIUrl":null,"url":null,"abstract":"We prove that distribution dependent (also called McKean--Vlasov) stochastic delay equations of the form \\begin{equation*} \\mathrm{d}X(t)= b(t,X_t,\\mathcal{L}_{X_t})\\mathrm{d}t+ \\sigma(t,X_t,\\mathcal{L}_{X_t})\\mathrm{d}W(t) \\end{equation*} have unique (strong) solutions in finite as well as infinite dimensional state spaces if the coefficients fulfill certain monotonicity assumptions.","PeriodicalId":8470,"journal":{"name":"arXiv: Probability","volume":"61 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Distribution-Dependent Stochastic Differential Delay Equations in finite and infinite dimensions\",\"authors\":\"Rico Heinemann\",\"doi\":\"10.1142/s0219025720500241\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that distribution dependent (also called McKean--Vlasov) stochastic delay equations of the form \\\\begin{equation*} \\\\mathrm{d}X(t)= b(t,X_t,\\\\mathcal{L}_{X_t})\\\\mathrm{d}t+ \\\\sigma(t,X_t,\\\\mathcal{L}_{X_t})\\\\mathrm{d}W(t) \\\\end{equation*} have unique (strong) solutions in finite as well as infinite dimensional state spaces if the coefficients fulfill certain monotonicity assumptions.\",\"PeriodicalId\":8470,\"journal\":{\"name\":\"arXiv: Probability\",\"volume\":\"61 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219025720500241\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219025720500241","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Distribution-Dependent Stochastic Differential Delay Equations in finite and infinite dimensions
We prove that distribution dependent (also called McKean--Vlasov) stochastic delay equations of the form \begin{equation*} \mathrm{d}X(t)= b(t,X_t,\mathcal{L}_{X_t})\mathrm{d}t+ \sigma(t,X_t,\mathcal{L}_{X_t})\mathrm{d}W(t) \end{equation*} have unique (strong) solutions in finite as well as infinite dimensional state spaces if the coefficients fulfill certain monotonicity assumptions.
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