Concentration inequalities for strong laws and laws of the iterated logarithm
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915589452201984 |
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| author | Ruf, Johannes Waudby-Smith, Ian |
| author_facet | Ruf, Johannes Waudby-Smith, Ian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concentration inequalities for strong laws and laws of the iterated logarithm Ruf, Johannes Waudby-Smith, Ian Probability Statistics Theory 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. |
| title | Concentration inequalities for strong laws and laws of the iterated logarithm |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2511.00175 |