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August, 1981 Weighted Sums of Independent Identically Distributed Random Variables
Ralf Ulbricht
Ann. Probab. 9(4): 693-698 (August, 1981). DOI: 10.1214/aop/1176994377


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.


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Ralf Ulbricht. "Weighted Sums of Independent Identically Distributed Random Variables." Ann. Probab. 9 (4) 693 - 698, August, 1981.


Published: August, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0467.60051
MathSciNet: MR624697
Digital Object Identifier: 10.1214/aop/1176994377

Primary: 60G50
Secondary: 46E30 , 60E05

Keywords: convergence of weighted sums a.e. , existence of sums in $L_p$ , identically distributed random variables , sequences of real numbers

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 4 • August, 1981
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