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.

...More
Included in

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

Citation URI
https://data.isiscb.org/isis/citation/CBB001021417/

Similar Citations

Article Lai, Tze Leung; (2009)
History of Martingales in Sequential Analysis and Time Series (/isis/citation/CBB001021425/)

Article Meyer, Paul-André; (2009)
Stochastic Processes from 1950 to the Present (/isis/citation/CBB001021423/)

Article Mazliak, Laurent; Shafer, Glenn; (2009)
Introduction (/isis/citation/CBB001021415/)

Article Mazliak, Laurent; (2009)
How Paul Lévy Saw Jean Ville and Martingales (/isis/citation/CBB001021419/)

Article Aalen, Odd; Andersen, Per Kragh; Borgan, Ørnulf; Gill, Richard; Keiding, Niels; (2009)
History of Applications of Martingales in Survival Analysis (/isis/citation/CBB001021426/)

Article Mazliak, Laurent; (2010)
Borel, Fréchet, Darmois: La découverte des statistiques par les probabilistes français (/isis/citation/CBB001024451/)

Article Watanabe, Shinzo; (2009)
Japanese Contributions to Martingale Theory (/isis/citation/CBB001021424/)

Article Regazzini, Eugenio; Spizzichino, Fabio; (2011)
De Finetti's Encounter with Martingales (/isis/citation/CBB001024469/)

Book Laurent Mazliak; Glenn Shafer; (2022)
The Splendors and Miseries of Martingales: Their History from the Casino to Mathematics (/isis/citation/CBB195334126/)

Article Bienvenu, Laurent; Shafer, Glenn; Shen, Alexander; (2009)
On the History of Martingales in the Study of Randomness (/isis/citation/CBB001021421/)

Article Catellier, Rémi; Mazliak, Laurent; (2012)
The Emergence of French Probabilistic Statistics. Borel and the Institut Henri Poincaré around the 1920s (/isis/citation/CBB001211451/)

Article Armatte, Michel; Desrosieres, Alain; (2010)
Paris Statistical Society Was Born 150 Years Ago (/isis/citation/CBB001024447/)

Article Meusnier, Norbert; (2006)
Sur l'histoire de l'enseignement des probabilités et des statistiques (/isis/citation/CBB000931993/)

Article Siegmund-Schultze, Reinhard; (2009)
The Institute Henri Poincaré and Mathematics in France between the Wars (/isis/citation/CBB000954527/)

Book Volterra, Vito; Mazliak, Laurent; Tazzioli, Rossana; (2009)
Mathematicians at War: Volterra and His French Colleagues in World War I (/isis/citation/CBB001251203/)

Article Courtebras, Bernard; (2006)
Probabilités et Statistiques dans l'enseignement secondaire de l'Occupation à la Libération (/isis/citation/CBB001021382/)

Article Schöttler, Peter; (2012)
Szientismus (/isis/citation/CBB001420906/)

Article Loredana Biacino; (2018)
The Concept of Function at the Beginning of the 20th Century: A Historiographical Approach (/isis/citation/CBB435431910/)

Authors & Contributors
Mazliak, Laurent
Shafer, Glenn
Watanabe, Shinzo
Volterra, Vito
Tazzioli, Rossana
Spizzichino, Fabio
Concepts
Mathematics
Probability and statistics
Martingales (mathematics)
Risk
Stochastic or random processes
Societies; institutions; academies
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
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment