Open Access
November, 1985 On Complete Convergence in the Law of Large Numbers for Subsequences
Allan Gut
Ann. Probab. 13(4): 1286-1291 (November, 1985). DOI: 10.1214/aop/1176992812


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.


Download Citation

Allan Gut. "On Complete Convergence in the Law of Large Numbers for Subsequences." Ann. Probab. 13 (4) 1286 - 1291, November, 1985.


Published: November, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0582.60057
MathSciNet: MR806225
Digital Object Identifier: 10.1214/aop/1176992812

Primary: 60F15
Secondary: 60G50

Keywords: complete convergence , i.i.d. random variables , Strong law of large numbers , subsequence

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 4 • November, 1985
Back to Top