Mazliak, Laurent (Author)
Shafer, Glenn (Author)
Over the past eighty years, martingales have become central in the mathematics of randomness. They appear in the general theory of stochastic processes, in the algorithmic theory of randomness, and in some branches of mathematical statistics. Yet little has been written about the history of this evolution. This book explores some of the territory that the history of the concept of martingales has transformed. The historian of martingales faces an immense task. We can find traces of martingale thinking at the very beginning of probability theory, because this theory was related to gambling, and the evolution of a gambler’s holdings as a result of following a particular strategy can always be understood as a martingale. More recently, in the second half of the twentieth century, martingales became important in the theory of stochastic processes at the very same time that stochastic processes were becoming increasingly important in probability, statistics and more generally in various applied situations. Moreover, a history of martingales, like a history of any other branch of mathematics, must go far beyond an account of mathematical ideas and techniques. It must explore the context in which the evolution of ideas took place: the broader intellectual milieux of the actors, the networks that already existed or were created by the research, even the social and political conditions that favored or hampered the circulation and adoption of certain ideas. This books presents a stroll through this history, in part a guided tour, in part a random walk. First, historical studies on the period from 1920 to 1950 are presented, when martingales emerged as a distinct mathematical concept. Then insights on the period from 1950 into the 1980s are offered, when the concept showed its value in stochastic processes, mathematical statistics, algorithmic randomness and various applications.
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Article
Bienvenu, Laurent;
Shafer, Glenn;
Shen, Alexander;
(2009)
On the History of Martingales in the Study of Randomness
(/isis/citation/CBB001021421/)
Article
Meyer, Paul-André;
(2009)
Stochastic Processes from 1950 to the Present
(/isis/citation/CBB001021423/)
Article
Lai, Tze Leung;
(2009)
History of Martingales in Sequential Analysis and Time Series
(/isis/citation/CBB001021425/)
Article
Watanabe, Shinzo;
(2009)
Japanese Contributions to Martingale Theory
(/isis/citation/CBB001021424/)
Article
Bru, Bernard;
Bru, Marie France;
Chung, Kai Lai;
(2009)
Borel and the St. Petersburg Martingale
(/isis/citation/CBB001021417/)
Article
Mazliak, Laurent;
(2009)
How Paul Lévy Saw Jean Ville and Martingales
(/isis/citation/CBB001021419/)
Article
Locker, Bernard;
(2009)
Doob at Lyon: On His Lecture, Application of the Theory of Martingales,at the Lyon Colloquium, June 28--July 3, 1948
(/isis/citation/CBB001021422/)
Article
Mazliak, Laurent;
Shafer, Glenn;
(2009)
Introduction
(/isis/citation/CBB001021415/)
Article
Regazzini, Eugenio;
Spizzichino, Fabio;
(2011)
De Finetti's Encounter with Martingales
(/isis/citation/CBB001024469/)
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
John Robinson;
Alan H. Welsh;
(2017)
Peter Gavin Hall 1951–2016
(/isis/citation/CBB683763240/)
Article
John Robinson;
Alan H. Welsh;
(2017)
Corrigendum to: Peter Gavin Hall 1951–2016
(/isis/citation/CBB180021568/)
Book
Rothstein, William G.;
(2003)
Public Health and the Risk Factor: A History of an Uneven Medical Revolution
(/isis/citation/CBB000320280/)
Article
Richey, Matthew;
(2010)
The Evolution of Markov Chain Monte Carlo Methods
(/isis/citation/CBB001211030/)
Article
McClelland, James L.;
(2012)
R. Duncan Luce (1925--2012)
(/isis/citation/CBB001320468/)
Article
Eugene Seneta;
(2018)
Joseph Mark Gani 1924–2016
(/isis/citation/CBB891098343/)
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David, H. A. (Herbert Aron);
Edwards, A. W. F. (Anthony William Fairbank);
(2000)
Annotated Readings in the History of Statistics
(/isis/citation/CBB000101937/)
Book
Hemmo, Meir;
Shenker, Orly R.;
(2012)
The Road to Maxwell's Demon, Conceptual Foundations of Statistical Mechanics
(/isis/citation/CBB001500356/)
Book
McGrayne, Sharon Bertsch;
(2011)
The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy
(/isis/citation/CBB001231898/)
Article
Aldrich, John;
(2010)
Mathematics in the London/Royal Statistical Society
(/isis/citation/CBB001021434/)
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