Article ID: CBB001021417

Borel and the St. Petersburg Martingale (2009)

unapi

Bru, Bernard (Author)
Bru, Marie-France (Author)
Chung, Kai Lai (Author)


Journal Electronique d'Histoire des Probabilités et de la Statistique
Volume: 5, no. 1
Issue: 1


Publication Date: 2009
Edition Details: http://www.jehps.net/juin2009/BruBruChung.pdf (Accessed on November 30, 2010). Part of a special issue, “The Splendors and Miseries of Martingales.”
Language: English

Thispaperexamines---bymeansoftheexampleoftheSt.Peters-burgparadox---howBorelexpositedthescienceofhisday.ThefirstpartsketchesthesingularplaceofpopularizationinBorel'swork.ThetwopartsthatfollowgiveachronologicalpresentationofBorel'scon-tributionstotheSt.Petersburgparadox,contributionsthatevolvedoveraperiodofmorethanfiftyyears.TheseshowhowBorelattackedtheproblembypositioningitinalong---andscientificallyveryrich---meditationontheparadoxofmartingales,thosesystemsofplaythatpurporttomakeagamblertossingacoinrich.Borelgaveanorigi-nalsolutiontothisproblem,anticipatingthefundamentalequalityofthenascentmathematicaltheoryofmartingales.TheparadoxicalroleplayedbyF'elixLeDantecinthedevelopmentofBorel'sthoughtonthesethemesishighlighted.AnappendixrecastsBorel'smartingalesinmodernterms.

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Article Mazliak, Laurent; Shafer, Glenn (2009) Introduction. Journal Electronique d'Histoire des Probabilités et de la Statistique. unapi

Citation URI
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Authors & Contributors
Mazliak, Laurent
Shafer, Glenn
Meusnier, Norbert
Siegmund-Schultze, Reinhard
Courtebras, Bernard
Bienvenu, Laurent
Journals
Journal Electronique d'Histoire des Probabilités et de la Statistique
Revue d'Histoire des Sciences
Revue d'Histoire des Mathématiques
Centaurus: International Magazine of the History of Mathematics, Science, and Technology
Foundations of Science
NTM: Zeitschrift für Geschichte der Naturwissenschaften, Technik und Medizin
Publishers
Springer
Concepts
Mathematics
Probability and statistics
Martingales (mathematics)
Risk
Science education and teaching
Societies; institutions; academies
People
Borel, Felix Édouard Émile
Fréchet, Maurice René
Ville, Jean-André
Volterra, Vito
Condorcet, Jean Antoine Nicolas Caritat, Marquis de
Lévy, Paul
Time Periods
20th century
20th century, early
19th century
20th century, late
18th century
Places
France
Japan
Italy
Institutions
Institut Henri Poincaré
École Polytechnique, Paris
Centre National de la Recherche Scientifique (France)
Société de Statistique de Paris
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