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Concentration inequalities for strong laws and laws of th...
[Submitted on 31 Oct 2025 (v1), last revised 8 Sep 2026 (this ve · 2025-11-01 · via math.ST updates on arXiv.org

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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.

Submission history

From: Ian Waudby-Smith [view email]
[v1] Fri, 31 Oct 2025 18:28:16 UTC (26 KB)
[v2] Tue, 8 Sep 2026 18:33:37 UTC (27 KB)

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