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
Watanabe, Shinzo
Volterra, Vito
Tazzioli, Rossana
Spizzichino, Fabio
Journals
Journal Electronique d'Histoire des Probabilités et de la Statistique
Transversal: International Journal for the Historiography of Science
Revue d'Histoire des Sciences
Revue d'Histoire des Mathématiques
Foundations of Science
Centaurus: International Magazine of the History of Mathematics, Science, and Technology
Publishers
Springer Nature
Springer
Concepts
Mathematics
Probability and statistics
Martingales (mathematics)
Risk
Stochastic or random processes
Societies; institutions; academies
People
Borel, Felix Édouard Émile
Fréchet, Maurice René
Volterra, Vito
Ville, Jean-André
Weierstrass, Karl Theodor
Wald, Abraham
Time Periods
20th century
20th century, early
19th century
20th century, late
21st century
18th century
Places
France
Japan
Italy
Institutions
Institut Henri Poincaré (France)
Société de Statistique de Paris
Centre National de la Recherche Scientifique (France)
École Polytechnique, Paris
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