Strong Laws of Large Numbers for Intermediately Trimmed Sums of i.i.d. Random Variables with Infinite Mean

  • Marc Kesseböhmer
  • Tanja Schindler


We show that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds. We provide an explicit procedure to find a moderate trimming sequence even if the underlying distribution function has a complicated structure, e.g., has no regularly varying tail distribution.


Almost sure convergence theorem Moderately trimmed sum Strong law of large numbers 

Mathematics Subject Classification (2010)

60F15 60G50 60G70 



We thank David Mason for mentioning the publications on trimmed sums for slowly varying tails, Péter Kevei for useful comments on an earlier draft of this paper and the referee for his or her valuable comments and careful proofreading which considerably improved the quality of this paper.


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Authors and Affiliations

  1. 1.Fachbereich 3 – Mathematik und InformatikUniversität BremenBremenGermany
  2. 2.Research School of Finance, Actuarial Studies and StatisticsAustralian National UniversityActonAustralia

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