{"title":"黎曼对称空间上的布朗桥","authors":"Philippe Bougerol, Thierry Jeulin","doi":"10.1016/S0764-4442(01)02145-0","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the Brownian bridge of length <em>T</em> on a symmetric space of the noncompact type. We prove that this process, properly rescaled, converges when <em>T</em>→+∞ to a process whose generalized radial part is the bridge of the Euclidean Brownian motion in the Weyl chamber killed at the boundary.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 785-790"},"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)02145-0","citationCount":"8","resultStr":"{\"title\":\"Brownian bridge on Riemannian symmetric spaces\",\"authors\":\"Philippe Bougerol, Thierry Jeulin\",\"doi\":\"10.1016/S0764-4442(01)02145-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the Brownian bridge of length <em>T</em> on a symmetric space of the noncompact type. We prove that this process, properly rescaled, converges when <em>T</em>→+∞ to a process whose generalized radial part is the bridge of the Euclidean Brownian motion in the Weyl chamber killed at the boundary.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 8\",\"pages\":\"Pages 785-790\"},\"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)02145-0\",\"citationCount\":\"8\",\"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/S0764444201021450\",\"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/S0764444201021450","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider the Brownian bridge of length T on a symmetric space of the noncompact type. We prove that this process, properly rescaled, converges when T→+∞ to a process whose generalized radial part is the bridge of the Euclidean Brownian motion in the Weyl chamber killed at the boundary.
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