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 $E \sup_k|S_{n_k}/n_k| < \infty$.
Publié le : 1979-12-14
Classification:
i.i.d. random variables,
subsequence,
expected supremum,
60F15
@article{1176994900,
author = {Gut, Allan},
title = {On the Integrability of $\sup|S\_n/n|$ for Subsequences},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 1059-1065},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994900}
}
Gut, Allan. On the Integrability of $\sup|S_n/n|$ for Subsequences. Ann. Probab., Tome 7 (1979) no. 6, pp. 1059-1065. http://gdmltest.u-ga.fr/item/1176994900/