Overview
- First book on the history of martingales
- Embeds a part of the history of probability in its context
- Includes contributions by renowned mathematicians and historians
Part of the book series: Trends in the History of Science (TRENDSHISTORYSCIENCE)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (19 chapters)
-
Front Matter
-
Ville, Lévy and Doob
-
Front Matter
-
-
Modern Probability
-
Front Matter
-
-
Documents
-
Front Matter
-
Keywords
About this book
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 invarious 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.Editors and Affiliations
About the editors
Glenn Shafer is Dean and Professor at the Rutgers Business School, Rutgers University, USA. He received an A.B. in mathematics in 1968 and a Ph.D. in mathematical statistics in 1973 from Princeton University, USA. He is best known for his work in the 1970s and 1980s on the Dempster-Shafer theory. It is a general framework for reasoning with uncertainty, allowing one to combine evidence from different sources and arrive at a degree of belief (represented by a mathematical object called belief function) that takes into account all the available evidence. The theory and its extensions have been of particular interest to the artificial intelligence community. More recently he worked with Vladimir Vovk to develop a game-theoretic framework for probability leafding to Probability and Finance: It's Only a Game! Glenn Shafer is also deeply interested in the history of mathematics (especially probability) and has authored several papers on the topic, such as a profound study of the origin of Kolmogorov's work on the foundation of probability with Vladimir Vovk, and a study about the arrest of Emile Borel during the German occupation of France with Laurent Mazliak.
Bibliographic Information
Book Title: The Splendors and Miseries of Martingales
Book Subtitle: Their History from the Casino to Mathematics
Editors: Laurent Mazliak, Glenn Shafer
Series Title: Trends in the History of Science
DOI: https://doi.org/10.1007/978-3-031-05988-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-05987-2Published: 18 October 2022
Softcover ISBN: 978-3-031-05990-2Published: 18 October 2023
eBook ISBN: 978-3-031-05988-9Published: 17 October 2022
Series ISSN: 2297-2951
Series E-ISSN: 2297-296X
Edition Number: 1
Number of Pages: XIV, 418
Number of Illustrations: 9 b/w illustrations, 8 illustrations in colour
Topics: History of Mathematical Sciences