{"title":"随机动力学方程的定量近似:从离散到连续","authors":"Zimo Hao, Khoa Lê, Chengcheng Ling","doi":"arxiv-2409.05706","DOIUrl":null,"url":null,"abstract":"We study the convergence of a generic tamed Euler-Maruyama (EM) scheme for\nthe kinetic type stochastic differential equations (SDEs) (also known as second\norder SDEs) with singular coefficients in both weak and strong probabilistic\nsenses. We show that when the drift exhibits a relatively low regularity\ncompared to the state of the art, the singular system is well-defined both in\nthe weak and strong probabilistic senses. Meanwhile, the corresponding tamed EM\nscheme is shown to converge at the rate of 1/2 in both the weak and the strong\nsenses.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantitative approximation of stochastic kinetic equations: from discrete to continuum\",\"authors\":\"Zimo Hao, Khoa Lê, Chengcheng Ling\",\"doi\":\"arxiv-2409.05706\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the convergence of a generic tamed Euler-Maruyama (EM) scheme for\\nthe kinetic type stochastic differential equations (SDEs) (also known as second\\norder SDEs) with singular coefficients in both weak and strong probabilistic\\nsenses. We show that when the drift exhibits a relatively low regularity\\ncompared to the state of the art, the singular system is well-defined both in\\nthe weak and strong probabilistic senses. Meanwhile, the corresponding tamed EM\\nscheme is shown to converge at the rate of 1/2 in both the weak and the strong\\nsenses.\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.05706\",\"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 - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05706","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quantitative approximation of stochastic kinetic equations: from discrete to continuum
We study the convergence of a generic tamed Euler-Maruyama (EM) scheme for
the kinetic type stochastic differential equations (SDEs) (also known as second
order SDEs) with singular coefficients in both weak and strong probabilistic
senses. We show that when the drift exhibits a relatively low regularity
compared to the state of the art, the singular system is well-defined both in
the weak and strong probabilistic senses. Meanwhile, the corresponding tamed EM
scheme is shown to converge at the rate of 1/2 in both the weak and the strong
senses.