Annals of Probability

Weighted Sums of Independent Identically Distributed Random Variables

Ralf Ulbricht

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Abstract

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.

Article information

Source
Ann. Probab., Volume 9, Number 4 (1981), 693-698.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994377

Digital Object Identifier
doi:10.1214/aop/1176994377

Mathematical Reviews number (MathSciNet)
MR624697

Zentralblatt MATH identifier
0467.60051

JSTOR
links.jstor.org

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60E05: Distributions: general theory 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

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

Citation

Ulbricht, Ralf. Weighted Sums of Independent Identically Distributed Random Variables. Ann. Probab. 9 (1981), no. 4, 693--698. doi:10.1214/aop/1176994377. https://projecteuclid.org/euclid.aop/1176994377


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