{"title":"采用深度后向动态程序设计时间行进的 Neumann 边界条件非线性 BSPDE 的局部非连续 Galerkin 方法","authors":"Yixiang Dai, Yunzhang Li, Jing Zhang","doi":"arxiv-2409.11004","DOIUrl":null,"url":null,"abstract":"This paper aims to present a local discontinuous Galerkin (LDG) method for\nsolving backward stochastic partial differential equations (BSPDEs) with\nNeumann boundary conditions. We establish the $L^2$-stability and optimal error\nestimates of the proposed numerical scheme. Two numerical examples are provided\nto demonstrate the performance of the LDG method, where we incorporate a deep\nlearning algorithm to address the challenge of the curse of dimensionality in\nbackward stochastic differential equations (BSDEs). The results show the\neffectiveness and accuracy of the LDG method in tackling BSPDEs with Neumann\nboundary conditions.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local discontinuous Galerkin method for nonlinear BSPDEs of Neumann boundary conditions with deep backward dynamic programming time-marching\",\"authors\":\"Yixiang Dai, Yunzhang Li, Jing Zhang\",\"doi\":\"arxiv-2409.11004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper aims to present a local discontinuous Galerkin (LDG) method for\\nsolving backward stochastic partial differential equations (BSPDEs) with\\nNeumann boundary conditions. We establish the $L^2$-stability and optimal error\\nestimates of the proposed numerical scheme. Two numerical examples are provided\\nto demonstrate the performance of the LDG method, where we incorporate a deep\\nlearning algorithm to address the challenge of the curse of dimensionality in\\nbackward stochastic differential equations (BSDEs). The results show the\\neffectiveness and accuracy of the LDG method in tackling BSPDEs with Neumann\\nboundary conditions.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11004\",\"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 - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Local discontinuous Galerkin method for nonlinear BSPDEs of Neumann boundary conditions with deep backward dynamic programming time-marching
This paper aims to present a local discontinuous Galerkin (LDG) method for
solving backward stochastic partial differential equations (BSPDEs) with
Neumann boundary conditions. We establish the $L^2$-stability and optimal error
estimates of the proposed numerical scheme. Two numerical examples are provided
to demonstrate the performance of the LDG method, where we incorporate a deep
learning algorithm to address the challenge of the curse of dimensionality in
backward stochastic differential equations (BSDEs). The results show the
effectiveness and accuracy of the LDG method in tackling BSPDEs with Neumann
boundary conditions.