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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

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

Information

Published: December, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0428.60036
MathSciNet: MR548901
Digital Object Identifier: 10.1214/aop/1176994900

Subjects:
Primary: 60F15

Keywords: expected supremum , i.i.d. random variables , subsequence

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 6 • December, 1979
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