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arXiv · 2511.00175

Concentration inequalities for strong laws and laws of the iterated logarithm

Johannes Ruf·Ian Waudby-Smith
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Abstract

We derive concentration inequalities for sums of independent and identically distributed random variables that yield non-asymptotic generalizations of several strong laws of large numbers including some of those due to Kolmogorov [1930], Marcinkiewicz and Zygmund [1937], Chung [1951], Baum and Katz [1965], Ruf, Larsson, Koolen, and Ramdas [2023], and Waudby-Smith, Larsson, and Ramdas [2024]. As applications, we derive non-asymptotic iterated logarithm inequalities in the spirit of Darling and Robbins [1967], as well as pathwise (sometimes described as "game-theoretic") analogues of strong laws and laws of the iterated logarithm.

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Johannes Ruf, Ian Waudby-Smith. 2025-10-31. Concentration inequalities for strong laws and laws of the iterated logarithm. https://arxiv.org/abs/2511.00175

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