Journal of Theoretical Probability

, Volume 17, Issue 3, pp 769–779 | Cite as

An Extension of the Kolmogorov–Feller Weak Law of Large Numbers with an Application to the St. Petersburg Game

Article

Abstract

The Kolmogorov–Feller weak law of large numbers for i.i.d. random variables without finite mean is extended to a larger class of distributions, requiring regularly varying normalizing sequences. As an application we show that the weak law of large numbers for the St. Petersburg game is an immediate consequence of our result.

Sums of i.i.d. random variables Feller WLLN slow variation regular variation 

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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • A. Gut
    • 1
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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