Concentration inequalities for strong laws and laws of the iterated logarithm

2025/10/31 by Ruf, Johannes, Waudby-Smith, Ian
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2511.00175

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.

Citations

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• Stein's method for concentration inequalities