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

Marc Kesseböhmer () and Tanja Schindler ()
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Marc Kesseböhmer: Universität Bremen
Tanja Schindler: Australian National University

Journal of Theoretical Probability, 2019, vol. 32, issue 2, 702-720

Abstract: Abstract 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.

Keywords: Almost sure convergence theorem; Moderately trimmed sum; Strong law of large numbers; 60F15; 60G50; 60G70 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-017-0802-0

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