{"title":"最优控制积分方程的概率解","authors":"M. Lefebvre","doi":"10.1216/jie.2022.34.215","DOIUrl":null,"url":null,"abstract":"A probabilistic interpretation of the exact solution of a certain inhomogeneous Fredholm integral equation of the second kind is given. Then, this interpretation is used to obtain an approximate solution of a generalization of the integral equation. The approximate solutions are compared with the corresponding Neumann series solutions in various particular cases. AMS Subject Classification: Primary 45B05; Secondary 62M10, 93E20.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Probabilistic solutions of integral equations from optimal control\",\"authors\":\"M. Lefebvre\",\"doi\":\"10.1216/jie.2022.34.215\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A probabilistic interpretation of the exact solution of a certain inhomogeneous Fredholm integral equation of the second kind is given. Then, this interpretation is used to obtain an approximate solution of a generalization of the integral equation. The approximate solutions are compared with the corresponding Neumann series solutions in various particular cases. AMS Subject Classification: Primary 45B05; Secondary 62M10, 93E20.\",\"PeriodicalId\":50176,\"journal\":{\"name\":\"Journal of Integral Equations and Applications\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Integral Equations and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1216/jie.2022.34.215\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Integral Equations and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1216/jie.2022.34.215","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Probabilistic solutions of integral equations from optimal control
A probabilistic interpretation of the exact solution of a certain inhomogeneous Fredholm integral equation of the second kind is given. Then, this interpretation is used to obtain an approximate solution of a generalization of the integral equation. The approximate solutions are compared with the corresponding Neumann series solutions in various particular cases. AMS Subject Classification: Primary 45B05; Secondary 62M10, 93E20.
期刊介绍：
Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications.
The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field.
The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.
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