{"title":"路径-分布相关随机哈密顿系统的指数遍历性与混沌的传播","authors":"Xing Huang, Wujun Lv","doi":"10.1214/23-ejp1027","DOIUrl":null,"url":null,"abstract":"By Girsanov’s theorem and using the existing log-Harnack inequality for distribution independent SDEs, the log-Harnack inequality is derived for path-distribution dependent stochastic Hamiltonian system. As an application, the exponential ergodicity in relative entropy is obtained by combining with transportation cost inequality. In addition, the quantitative propagation of chaos in the sense of Wasserstein distance is obtained, which together with the coupling by change of measure implies the quantitative propagation of chaos in total variation norm as well as relative entropy.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Exponential ergodicity and propagation of chaos for path-distribution dependent stochastic Hamiltonian system\",\"authors\":\"Xing Huang, Wujun Lv\",\"doi\":\"10.1214/23-ejp1027\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"By Girsanov’s theorem and using the existing log-Harnack inequality for distribution independent SDEs, the log-Harnack inequality is derived for path-distribution dependent stochastic Hamiltonian system. As an application, the exponential ergodicity in relative entropy is obtained by combining with transportation cost inequality. In addition, the quantitative propagation of chaos in the sense of Wasserstein distance is obtained, which together with the coupling by change of measure implies the quantitative propagation of chaos in total variation norm as well as relative entropy.\",\"PeriodicalId\":50538,\"journal\":{\"name\":\"Electronic Journal of Probability\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/23-ejp1027\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/23-ejp1027","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Exponential ergodicity and propagation of chaos for path-distribution dependent stochastic Hamiltonian system
By Girsanov’s theorem and using the existing log-Harnack inequality for distribution independent SDEs, the log-Harnack inequality is derived for path-distribution dependent stochastic Hamiltonian system. As an application, the exponential ergodicity in relative entropy is obtained by combining with transportation cost inequality. In addition, the quantitative propagation of chaos in the sense of Wasserstein distance is obtained, which together with the coupling by change of measure implies the quantitative propagation of chaos in total variation norm as well as relative entropy.
期刊介绍:
The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory.
Both ECP and EJP are official journals of the Institute of Mathematical Statistics
and the Bernoulli society.