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The Splendors and Miseries of Martingales : Their History from the Casino to Mathematics /

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 evo...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Mazliak, Laurent (Editor), Shafer, Glenn (Editor)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2022.
Edition:1st ed. 2022.
Series:Trends in the History of Science,
Subjects:
Mathematics.
History.
History of Mathematical Sciences.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • IN THE BEGINNING: 1. Roger Mansuy: The Origins and Multiple Meanings of Martingale
  • 2. Glenn Shafer: Martingales at the Casino
  • 3. Bernard Bru and Marie-France Bru: Emile Borel's Denumerable Martingales, 1909-1949
  • 4. Salah Eid: The Dawn of Martingale Convergence: Jessen's Theorem and Lévy's Lemma
  • VILLE, LEVY and DOOB: 5. Glenn Shafer: Did Jean Ville Invent Martingales?
  • 6. Laurent Mazliak: Paul Lévy's Perspective on Martingales and on Jean Ville
  • 7. Bernard Locker and Laurent Mazliak: Doob at Lyon: Bringing Martingales Back to France
  • MODERN PROBABILITY: 8. Paul-André Meyer and Glenn Shafer: Stochastic Processes in the Decades after 1950
  • 9. Shinzo Watanabe: Martingales in Japan
  • 10. Klaus Krickeberg: My Encounters with Martingales
  • MODERN APPLICATIONS: 11. Laurent Bienvenu, Glenn Shafer and Alexander Shen: Martingales in the Study of Randomness
  • 12. Tze Leung Lai: Encounters with Martingales in Statistics and Stochastic Optimization
  • 13. Odd O. Aalen, Per K. Andersen, Ørnulf Borgan, Richard D. Gill and Nils Keiding: Martingales in Survival Analysis
  • 14. Tyron Duncan: Encounters with Martingales in Stochastic Control. Appendix by Laurent Mazliak
  • DOCUMENTS: 15. Bernard Bru and Salah Eid: Analysis or Probability? Eight Letters between Børge Jessen and Paul Lévy
  • 16. Bernard Bru and Salah Eid: Counterexamples to Abstract Probability. Ten Letters by Jessen, Doob, and Dieudonné
  • 17. Pierre Crepel: Jean Ville Remembers Martingales
  • 18. Laurent Mazliak: Seven Letters from Paul Lévy to Maurice Fréchet
  • 19. Laurent Bienvenu, Glenn Shafer and Alexander Shen: Andrei Kolmogorov and Leonid Levin on Randomness. .