On Strong Convergence for Weighted Sums of a Class of Random VariablesReport as inadecuate




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Abstract and Applied AnalysisVolume 2013 2013, Article ID 216236, 7 pages

Research ArticleSchool of Mathematical Science, Anhui University, Hefei 230601, China

Received 5 February 2013; Accepted 27 February 2013

Academic Editor: Simeon Reich

Copyright © 2013 Aiting Shen. 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

Let be a sequence of random variables satisfying the Rosenthal-type maximal inequality. Complete convergence is studied for linear statistics that are weighted sums of identically distributed random variables under a suitable moment condition. As an application, the Marcinkiewicz-Zygmund-type strong law of large numbers is obtained. Our result generalizes the corresponding one of Zhou et al. 2011 and improves the corresponding one of Wang et al. 2011, 2012.





Author: Aiting Shen

Source: https://www.hindawi.com/



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