Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 168081, 11 pages
doi:10.1155/2010/168081
Research Article

Convergence Theorems for Partial Sums of Arbitrary Stochastic Sequences

Xiaosheng Wang and Haiying Guo

College of Science, Hebei University of Engineering, Handan 056038, China

Received 27 May 2010; Revised 24 September 2010; Accepted 20 October 2010

Academic Editor: Jewgeni Dshalalow

Copyright © 2010 Xiaosheng Wang and Haiying Guo. 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

By using Doob's martingale convergence theorem, this paper presents a class of strong limit theorems for arbitrary stochastic sequence. Chow's two strong limit theorems for martingale-difference sequence and Loève's and Petrov's strong limit theorems for independent random variables are the particular cases of the main results.