文章基本信息
- 标题：Borel and the St Petersburg Martingale
- 本地全文：下载
- 作者：Bernard Bru ; Marie France Bru ; Kai Lai Chung 等
- 期刊名称：Electronic Journal for History of Probability and Statistics
- 印刷版ISSN：1773-0074
- 电子版ISSN：1773-0074
- 出版年度：2009
- 卷号：5
- 期号：01
- 出版社：Ecole des Hautes Etudes en Sciences Sociales
- 摘要：
Thispaperexamines—bymeansoftheexampleoftheSt.Peters-burgparadox—howBorelexpositedthescienceofhisday.ThefirstpartsketchesthesingularplaceofpopularizationinBorel’swork.ThetwopartsthatfollowgiveachronologicalpresentationofBorel’scon-tributionstotheSt.Petersburgparadox,contributionsthatevolvedoveraperiodofmorethanfiftyyears.TheseshowhowBorelattackedtheproblembypositioningitinalong—andscientificallyveryrich—meditationontheparadoxofmartingales,thosesystemsofplaythatpurporttomakeagamblertossingacoinrich.Borelgaveanorigi-nalsolutiontothisproblem,anticipatingthefundamentalequalityofthenascentmathematicaltheoryofmartingales.TheparadoxicalroleplayedbyF´elixLeDantecinthedevelopmentofBorel’sthoughtonthesethemesishighlighted.AnappendixrecastsBorel’smartingalesinmodernterms.
