{"title":"随机变量的局部不变性原理","authors":"Jean-Christophe Breton, Youri Davydov","doi":"10.1016/S0764-4442(01)02112-7","DOIUrl":null,"url":null,"abstract":"<div><p>For a sequence of independent identically distributed random variables, the normalized step-processes associated are weakly convergent to the Wiener process. We strengthen for the functional distributions the convergence for the variation distance for a class of functionals.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 673-676"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02112-7","citationCount":"2","resultStr":"{\"title\":\"Principe local d'invariance pour des variables aléatoires i.i.d.\",\"authors\":\"Jean-Christophe Breton, Youri Davydov\",\"doi\":\"10.1016/S0764-4442(01)02112-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For a sequence of independent identically distributed random variables, the normalized step-processes associated are weakly convergent to the Wiener process. We strengthen for the functional distributions the convergence for the variation distance for a class of functionals.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 7\",\"pages\":\"Pages 673-676\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02112-7\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021127\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021127","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Principe local d'invariance pour des variables aléatoires i.i.d.
For a sequence of independent identically distributed random variables, the normalized step-processes associated are weakly convergent to the Wiener process. We strengthen for the functional distributions the convergence for the variation distance for a class of functionals.
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