Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-03T18:27:14.845Z Has data issue: false hasContentIssue false
  • English
  • Français

BERNOULLI'S LAW OF LARGE NUMBERS

Published online by Cambridge University Press:  18 June 2013

Erwin Bolthausen  and
Mario V. Wüthrich
Erwin Bolthausen
Affiliation:
University of Zurich, Institut für Mathematik, 8057 Zurich, Switzerlandeb@math.uzh.ch
Mario V. Wüthrich*
Affiliation:
ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland
*
mario.wuethrich@math.ethz.ch
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This year we celebrate the 300th anniversary of Jakob Bernoulli's path-breaking work Ars conjectandi, which appeared in 1713, eight years after his death. In Part IV of his masterpiece, Bernoulli proves the law of large numbers which is one of the fundamental theorems in probability theory, statistics and actuarial science. We review and comment on his original proof.

Keywords

Bernoullilaw of large numbersLLN
Type
Editorial
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 2 , May 2013 , pp. 73 - 79
Copyright
Copyright © ASTIN Bulletin 2013 

References

[1]Bernoulli, J. (1899) Wahrscheinlichkeitsrechnung (Ars conjectandi, 1713). In Ostwalds Klassiker der exakten Wissenschaften. Leipzig, Germany: W. Engelmann.Google Scholar
[2]Bernoulli, N. (1975) Usu Artis conjectandi in Jure. Doctoral Thesis, Basel 1709. In Die Werke von Jakob Bernoulli, Vol. 3, pp. 287–326. Basel, Switzerland: Birkhäuser.Google Scholar
[3]Bolthausen, E. (2010) Bernoullis Gesetz der grossen Zahlen. Elemente der Mathematik, 65, 134–143.CrossRefGoogle Scholar
[4]Khinchin, A. (1929) Sur la loi des grands nombres. Comptes rendus de l'Académie des Sciences, 189, 477–479.Google Scholar
[5]Kohli, K. (1975a) Aus dem Briefwechsel zwischen Leibniz und Jakob Bernoulli. In Die Werke von Jakob Bernoulli, Vol. 3, pp. 509–513. Basel, Switzerland: Birkhäuser.CrossRefGoogle Scholar
[6]Kohli, K. (1975b) Kommentar zur Dissertation von Niklaus Bernoulli. In Die Werke von Jakob Bernoulli, Vol. 3, pp. 541–557. Basel, Switzerland: Birkhäuser.CrossRefGoogle Scholar
[7]Stigler, S.M. (1986) The History of Statistics: The Measurement of Uncertainty before 1900. Cambridge, MA: The Belknap Press of the Harvard University Press.Google Scholar