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The Splendors and Miseries of MartingalesDoob at Lyon: Bringing Martingales Back to France

The Splendors and Miseries of Martingales: Doob at Lyon: Bringing Martingales Back to France [The evolution of Joseph Leo Doob’s work on probability is examined from the vantage point of his lecture on applications of the theory of martingales at the colloquium on probability at Lyon in 1948. During the 1940s, Doob had developed the theory of stochastic processes in Kolmogorov’s framework. In particular, he had built on Paul Lévy’s and Jean Ville’s work to develop a theory of martingales. At Lyon, he used his martingale convergence theorem, which he had already proven in 1940, to derive the strong law of large numbers and the almost sure consistency of Bayesian estimation. This article discusses the inception of the Lyon colloquium, Lévy’s and Ville’s work on martingales, Doob’s work in the 1940s, and finally the interactions at the colloquium and Doob’s lecture there. This lecture can be seen as bringing martingales back to France, the country of their origin. But the time was not yet ripe for French mathematicians to rise to the challenge they presented.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesDoob at Lyon: Bringing Martingales Back to France

Part of the Trends in the History of Science Book Series
Editors: Mazliak, Laurent; Shafer, Glenn
Locker, Bernard; Mazliak, Laurent
The Splendors and Miseries of Martingales — Oct 18, 2022
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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-031-05987-2
Pages
147 –166
DOI
10.1007/978-3-031-05988-9_7
Publisher site
See Chapter on Publisher Site

Abstract

[The evolution of Joseph Leo Doob’s work on probability is examined from the vantage point of his lecture on applications of the theory of martingales at the colloquium on probability at Lyon in 1948. During the 1940s, Doob had developed the theory of stochastic processes in Kolmogorov’s framework. In particular, he had built on Paul Lévy’s and Jean Ville’s work to develop a theory of martingales. At Lyon, he used his martingale convergence theorem, which he had already proven in 1940, to derive the strong law of large numbers and the almost sure consistency of Bayesian estimation. This article discusses the inception of the Lyon colloquium, Lévy’s and Ville’s work on martingales, Doob’s work in the 1940s, and finally the interactions at the colloquium and Doob’s lecture there. This lecture can be seen as bringing martingales back to France, the country of their origin. But the time was not yet ripe for French mathematicians to rise to the challenge they presented.]

Published: Oct 18, 2022

Keywords: History of probability; Martingales; Paul Lévy; Jean Ville; Joseph Doob; Lyon colloquium; Martingale convergence theorem; Strong law of large numbers; Bayesian estimation

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