## Abstract and Applied Analysis

### On Strong Convergence for Weighted Sums of a Class of Random Variables

Aiting Shen

#### Abstract

Let $\left\{{X}_{n},n\ge 1\right\}$ 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).

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 216236, 7 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511804

Digital Object Identifier
doi:10.1155/2013/216236

Mathematical Reviews number (MathSciNet)
MR3035392

Zentralblatt MATH identifier
1279.60041

#### Citation

Shen, Aiting. On Strong Convergence for Weighted Sums of a Class of Random Variables. Abstr. Appl. Anal. 2013 (2013), Article ID 216236, 7 pages. doi:10.1155/2013/216236. https://projecteuclid.org/euclid.aaa/1393511804

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