{"title":"Brownian motion conditioned to stay in a cone","authors":"Rodolphe Garbit","doi":"10.1215/KJM/1260975039","DOIUrl":null,"url":null,"abstract":"A result of R. Durrett, D. Iglehart and D. Miller states that Brownian meander is Brownian motion conditioned to stay positive for a unit of time, in the sense that it is the weak limit, as $x$ goes to $0$, of Brownian motion started at $x>0$ and conditioned to stay positive for a unit of time. We extend this limit theorem to the case of multidimensional Brownian motion conditioned to stay in a smooth convex cone.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"49 1","pages":"573-592"},"PeriodicalIF":0.0000,"publicationDate":"2008-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics of Kyoto University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1215/KJM/1260975039","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 16
Abstract
A result of R. Durrett, D. Iglehart and D. Miller states that Brownian meander is Brownian motion conditioned to stay positive for a unit of time, in the sense that it is the weak limit, as $x$ goes to $0$, of Brownian motion started at $x>0$ and conditioned to stay positive for a unit of time. We extend this limit theorem to the case of multidimensional Brownian motion conditioned to stay in a smooth convex cone.
期刊介绍：
Papers on pure and applied mathematics intended for publication in the Kyoto Journal of Mathematics should be written in English, French, or German. Submission of a paper acknowledges that the paper is original and is not submitted elsewhere.
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