{"title":"集合值超马太尔的莫斯科收敛性","authors":"M’hamed El-Louh, Fatima Ezzaki","doi":"10.1007/s43036-024-00340-x","DOIUrl":null,"url":null,"abstract":"<div><p>The existence of regular martingale selectors for multivalued supermartingales with unbounded values in a separable Banach space <i>Y</i> is proved. In addition, new convergence results for set-valued supermartingales in the Mosco sense are presented. At the end of this paper, the equivalence between some properties of unbounded set-valued supermartingales and the convergence of these random sets in the Mosco sense is established.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mosco convergence of set-valued supermartingale\",\"authors\":\"M’hamed El-Louh, Fatima Ezzaki\",\"doi\":\"10.1007/s43036-024-00340-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The existence of regular martingale selectors for multivalued supermartingales with unbounded values in a separable Banach space <i>Y</i> is proved. In addition, new convergence results for set-valued supermartingales in the Mosco sense are presented. At the end of this paper, the equivalence between some properties of unbounded set-valued supermartingales and the convergence of these random sets in the Mosco sense is established.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"9 3\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-024-00340-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00340-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
证明了在可分离的巴拿赫空间 Y 中具有无界值的多值超马尔廷态的正则马汀态选择器的存在性。此外，本文还提出了 Mosco 意义上的集合值超马丁定理的新收敛结果。最后，本文建立了无界集值超马尔廷阶的某些性质与这些随机集在 Mosco 意义上的收敛性之间的等价性。
The existence of regular martingale selectors for multivalued supermartingales with unbounded values in a separable Banach space Y is proved. In addition, new convergence results for set-valued supermartingales in the Mosco sense are presented. At the end of this paper, the equivalence between some properties of unbounded set-valued supermartingales and the convergence of these random sets in the Mosco sense is established.
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