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The Splendors and Miseries of MartingalesAnalysis or Probability? Eight Letters Between Børge Jessen and Paul Lévy

The Splendors and Miseries of Martingales: Analysis or Probability? Eight Letters Between Børge... [From September 1934 to August 1935, Børge Jessen and Paul Lévy exchanged eight letters, three from Jessen and five from Lévy, concerning the relation between what we now call Jessen’s theorem and Lévy’s lemma. Each contended, with some justice, that the other’s results could be derived from their own, and we now think of both as versions of the martingale convergence theorem. Jessen’s and Lévy’s contrasting viewpoints are analyzed in detail in this volume’s chapter entitled “The Dawn of Martingale Convergence: Jessen’s Theorem and Lévy’s Lemma’, by Salah Eid. Here we present the letters and drafts that have survived in the Jessen archives at the University of Copenhagen. Jessen’s first letter is missing, but we have Lévy’s five letters and drafts of two of Jessen’s letters. We also include a 1947 letter from Harald Bohr and Jessen to Lévy, which does not to the mathematical discussion but shows the continued relationship between the parties.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesAnalysis or Probability? Eight Letters Between Børge Jessen and Paul Lévy

Part of the Trends in the History of Science Book Series
Editors: Mazliak, Laurent; Shafer, Glenn

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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
337 –360
DOI
10.1007/978-3-031-05988-9_15
Publisher site
See Chapter on Publisher Site

Abstract

[From September 1934 to August 1935, Børge Jessen and Paul Lévy exchanged eight letters, three from Jessen and five from Lévy, concerning the relation between what we now call Jessen’s theorem and Lévy’s lemma. Each contended, with some justice, that the other’s results could be derived from their own, and we now think of both as versions of the martingale convergence theorem. Jessen’s and Lévy’s contrasting viewpoints are analyzed in detail in this volume’s chapter entitled “The Dawn of Martingale Convergence: Jessen’s Theorem and Lévy’s Lemma’, by Salah Eid. Here we present the letters and drafts that have survived in the Jessen archives at the University of Copenhagen. Jessen’s first letter is missing, but we have Lévy’s five letters and drafts of two of Jessen’s letters. We also include a 1947 letter from Harald Bohr and Jessen to Lévy, which does not to the mathematical discussion but shows the continued relationship between the parties.]

Published: Oct 18, 2022

Keywords: Børge Jessen; History of probability; Jessen’s theorem; Lévy’s lemma; Martingale convergence theorem; Lévy; Transfer principle

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