{"title":"斯坦-狄利克雷-马利文方法","authors":"L. Decreusefond","doi":"10.1051/PROC/201551003","DOIUrl":null,"url":null,"abstract":"The Stein's method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of the semi-group or of the smart-path method used commonly in Gaussian analysis. We show how this procedure can be enriched by Malliavin calculus leading to a functional approach valid in infinite dimensional spaces.","PeriodicalId":8470,"journal":{"name":"arXiv: Probability","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2015-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"The Stein-Dirichlet-Malliavin method\",\"authors\":\"L. Decreusefond\",\"doi\":\"10.1051/PROC/201551003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Stein's method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of the semi-group or of the smart-path method used commonly in Gaussian analysis. We show how this procedure can be enriched by Malliavin calculus leading to a functional approach valid in infinite dimensional spaces.\",\"PeriodicalId\":8470,\"journal\":{\"name\":\"arXiv: Probability\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-05-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/PROC/201551003\",\"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: Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/PROC/201551003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Stein's method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of the semi-group or of the smart-path method used commonly in Gaussian analysis. We show how this procedure can be enriched by Malliavin calculus leading to a functional approach valid in infinite dimensional spaces.
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