{"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}
引用次数: 3
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.
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