We characterize the sequences $(\alpha_i)$ of real numbers such that $\sum^\infty_{i = 1} \alpha_i f_i$ exists a.e. or in $L_p$ for all sequences of independent identically distributed symmetric random variables with $p$th moment. Moreover, we also treat the case $\sup|\alpha_i f_i| < 0\infty$ a.e.
Publié le : 1981-08-14
Classification:
Identically distributed random variables,
convergence of weighted sums a.e.,
existence of sums in $L_p$,
sequences of real numbers,
60G50,
60E05,
46E30
@article{1176994377,
author = {Ulbricht, Ralf},
title = {Weighted Sums of Independent Identically Distributed Random Variables},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 693-698},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994377}
}
Ulbricht, Ralf. Weighted Sums of Independent Identically Distributed Random Variables. Ann. Probab., Tome 9 (1981) no. 6, pp. 693-698. http://gdmltest.u-ga.fr/item/1176994377/