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The Splendors and Miseries of MartingalesStochastic Processes in the Decades after 1950

The Splendors and Miseries of Martingales: Stochastic Processes in the Decades after 1950 [Paul-André Meyer (1934–2003), founder and leader of the Strasbourg school of probability, worked from the 1960s into the 1990s on the theory of stochastic processes, emphasizing processes in continuous time. In this sweeping review, which first appeared in French in 2000, Meyer emphasizes the founding role of Doob’s Stochastic Processes, published in 1953, which presented tools and topics that fueled probabilistic research for the rest of the century: filtrations, stopping times, martingales, Markov processes, diffusions, Itô’s stochastic integral, and stochastic differential equations. The review then concentrates on two periods of research. The period from 1950 to 1965 was dominated by the study of Markov processes and their connections with potential theory and martingales. In the period from 1965 to 1980, martingales became more prominent, along with the stochastic integral, excursions, the general theory of processes, and stochastic mechanics. The review extends into the 1980s, discussing the Malliavin calculus and noncommutative probability theory. The great contributions by Doob and Itô are given their due.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesStochastic Processes in the Decades after 1950

Part of the Trends in the History of Science Book Series
Editors: Mazliak, Laurent; Shafer, Glenn
Meyer, Paul-André; Shafer, Glenn
The Splendors and Miseries of Martingales — Oct 18, 2022
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References (3)

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    Annals of Mathematical Statistics, 37

  • L Accardi (1982)

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    Publications of the Research Institute for Mathematical Sciences, Kyoto, 18

  • D Aldous (1978)

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    The Annals of Probability, 6

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
169 –202
DOI
10.1007/978-3-031-05988-9_8
Publisher site
See Chapter on Publisher Site

Abstract

[Paul-André Meyer (1934–2003), founder and leader of the Strasbourg school of probability, worked from the 1960s into the 1990s on the theory of stochastic processes, emphasizing processes in continuous time. In this sweeping review, which first appeared in French in 2000, Meyer emphasizes the founding role of Doob’s Stochastic Processes, published in 1953, which presented tools and topics that fueled probabilistic research for the rest of the century: filtrations, stopping times, martingales, Markov processes, diffusions, Itô’s stochastic integral, and stochastic differential equations. The review then concentrates on two periods of research. The period from 1950 to 1965 was dominated by the study of Markov processes and their connections with potential theory and martingales. In the period from 1965 to 1980, martingales became more prominent, along with the stochastic integral, excursions, the general theory of processes, and stochastic mechanics. The review extends into the 1980s, discussing the Malliavin calculus and noncommutative probability theory. The great contributions by Doob and Itô are given their due.]

Published: Oct 18, 2022

Keywords: General theory of processes; Malliavin calculus; Markov processes; Martingales; Noncommutative probability; Potential theory; Stochastic differential geometry; Stochastic integral; Stochastic processes; Stochastic processes; White noise

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