Journal of Applied Mathematics

Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of $\stackrel{~}{\rho }$-Mixing Random Variables

Chongfeng Lan

Abstract

The equivalent conditions of complete convergence are established for weighted sums of $\stackrel{~}{\rho }$-mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence of $\stackrel{~}{\rho }$-mixing random variables is obtained.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 612140, 8 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305617

Digital Object Identifier
doi:10.1155/2014/612140

Mathematical Reviews number (MathSciNet)
MR3187046

Citation

Lan, Chongfeng. Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of $\stackrel{~}{\rho }$ -Mixing Random Variables. J. Appl. Math. 2014 (2014), Article ID 612140, 8 pages. doi:10.1155/2014/612140. https://projecteuclid.org/euclid.jam/1425305617

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