Bernard De Meyer , Bernard Roynette , Pierre Vallois , Marc Yor
{"title":"Sur l'indépendance d'un temps d'arrêt T et de la position BT d'un mouvement brownien (Bu,u⩾0)","authors":"Bernard De Meyer , Bernard Roynette , Pierre Vallois , Marc Yor","doi":"10.1016/S0764-4442(01)02168-1","DOIUrl":null,"url":null,"abstract":"<div><p>In this Note, we describe many examples of two-dimensional random variables {<em>B</em><sub><em>T</em></sub>,<em>T</em>} obtained from the position of a Brownian motion <span><math><mtext>(B</mtext><msub><mi></mi><mn>t</mn></msub><mtext>;</mtext><mspace></mspace><mtext>t⩾0)</mtext></math></span> at a stopping time <em>T</em> such that <em>T</em> and <em>B</em><sub><em>T</em></sub> are independent. For such pairs, the law of <em>T</em> determines that of <em>B</em><sub><em>T</em></sub> and vice versa; we study the constraints on these laws induced by the independence assumption.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 1017-1022"},"PeriodicalIF":0.0000,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02168-1","citationCount":"1","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/S0764444201021681","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this Note, we describe many examples of two-dimensional random variables {BT,T} obtained from the position of a Brownian motion at a stopping time T such that T and BT are independent. For such pairs, the law of T determines that of BT and vice versa; we study the constraints on these laws induced by the independence assumption.
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