On the Integrability of $\sup|S_n/n|$ for Subsequences

Allan Gut

doi:10.1214/aop/1176994900

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Home > Journals > Ann. Probab. > Volume 7 > Issue 6 > Article

December, 1979 On the Integrability of $\sup|S_n/n|$ for Subsequences

Allan Gut

Ann. Probab. 7(6): 1059-1065 (December, 1979). DOI: 10.1214/aop/1176994900

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Abstract

Let $\{S_n; n \geqslant 1\}$ denote the partial sums of i.i.d. random variables and let $\{n_k; k \geqslant 1\}$ be a (strictly) increasing subsequence of the positive integers. We determine necessary and sufficient conditions for $E \sup_k|S_{n_k}/n_k| < \infty$.

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Allan Gut. "On the Integrability of $\sup|S_n/n|$ for Subsequences." Ann. Probab. 7 (6) 1059 - 1065, December, 1979. https://doi.org/10.1214/aop/1176994900