The Annals of Probability

A Limit Theorem for Double Arrays

Andrew Rosalsky and Henry Teicher

Full-text: Open access

Abstract

The main result establishes that row sums $S_n$ of a double array of rowwise independent, infinitesimal (or merely uniformly asymptotically constant) random variables satisfying $\lim \sup |S_n - M_n| \leq M_0 < \infty$ a.c. (for some choice of constants $M_n$), obey a weak law of large numbers, i.e., $S_n - \operatorname{med} S_n$ converges in probability to 0. No moment assumptions are imposed on the individual summands and zero-one laws are unavailable. As special cases, a new result for weighted i.i.d. random variables and a result of Kesten are obtained.

Article information

Source
Ann. Probab., Volume 9, Number 3 (1981), 460-467.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994418

Digital Object Identifier
doi:10.1214/aop/1176994418

Mathematical Reviews number (MathSciNet)
MR614630

Zentralblatt MATH identifier
0479.60034

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F15: Strong theorems

Keywords
Law of the iterated logarithm weak law of large numbers row sums of independent infinitesimal random variables weighted i.i.d. random variables

Citation

Rosalsky, Andrew; Teicher, Henry. A Limit Theorem for Double Arrays. Ann. Probab. 9 (1981), no. 3, 460--467. doi:10.1214/aop/1176994418. https://projecteuclid.org/euclid.aop/1176994418


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