Copyright © 2009 Qunying Wu and Yuanying Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study almost sure convergence for ρ˜-mixing sequences of random variables. Many of the previous results are our special cases. For example, the authors extend and improve the corresponding results of Chen et al. (1996) and Wu and Jiang (2008). We extend the classical Jamison convergence theorem and the Marcinkiewicz strong law of large numbers for independent sequences of random variables to ρ˜-mixing sequences of random variables without necessarily adding any extra conditions.