The Annals of Probability

On Complete Convergence in the Law of Large Numbers for Subsequences

Allan Gut

Full-text: Open access

Abstract

Shorter and more elementary proofs of some results of Asmussen and Kurtz are given. We determine first those subsequences for which mean zero is the necessary and sufficient requirement for complete convergence and then give integrability conditions in terms of the growth of the subsequences in the case when a moment of order greater than one exists.

Article information

Source
Ann. Probab., Volume 13, Number 4 (1985), 1286-1291.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992812

Digital Object Identifier
doi:10.1214/aop/1176992812

Mathematical Reviews number (MathSciNet)
MR806225

Zentralblatt MATH identifier
0582.60057

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 60G50: Sums of independent random variables; random walks

Keywords
Complete convergence subsequence i.i.d. random variables strong law of large numbers

Citation

Gut, Allan. On Complete Convergence in the Law of Large Numbers for Subsequences. Ann. Probab. 13 (1985), no. 4, 1286--1291. doi:10.1214/aop/1176992812. https://projecteuclid.org/euclid.aop/1176992812


Export citation