{"title":"路径依赖的汉密尔顿-雅各比-贝尔曼 PDE 的 Crandall-Lions 粘度解的收敛定理","authors":"David Criens","doi":"10.1007/s00030-024-00986-9","DOIUrl":null,"url":null,"abstract":"<p>We establish a convergence theorem for Crandall–Lions viscosity solutions to path-dependent Hamilton–Jacobi–Bellman PDEs. Our proof is based on a novel convergence theorem for dynamic sublinear expectations and the stochastic representation of viscosity solutions as value functions.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A convergence theorem for Crandall–Lions viscosity solutions to path-dependent Hamilton–Jacobi–Bellman PDEs\",\"authors\":\"David Criens\",\"doi\":\"10.1007/s00030-024-00986-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We establish a convergence theorem for Crandall–Lions viscosity solutions to path-dependent Hamilton–Jacobi–Bellman PDEs. Our proof is based on a novel convergence theorem for dynamic sublinear expectations and the stochastic representation of viscosity solutions as value functions.</p>\",\"PeriodicalId\":501665,\"journal\":{\"name\":\"Nonlinear Differential Equations and Applications (NoDEA)\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Differential Equations and Applications (NoDEA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00030-024-00986-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Differential Equations and Applications (NoDEA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00030-024-00986-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A convergence theorem for Crandall–Lions viscosity solutions to path-dependent Hamilton–Jacobi–Bellman PDEs
We establish a convergence theorem for Crandall–Lions viscosity solutions to path-dependent Hamilton–Jacobi–Bellman PDEs. Our proof is based on a novel convergence theorem for dynamic sublinear expectations and the stochastic representation of viscosity solutions as value functions.
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